Alternative words for “parts” of a bi-partite graph
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2
down vote
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Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example:
One "part" of the $K_{4,4}$ connects to a corresponding "part" of a
different graph while the other "part" does
not.
What are the synonyms (if any) that could be appropriate for replacing the word "part" here?
I am writing a paper for a very non-mathematical audience. This small community of researchers have come to learn what $K_{4,4}$ means, because it comes up often, but they have no other graph theory training and it will not be clear to them what "part" means. For example, the English word "part" could describe things like individual "vertices" or "edges". If the reader thinks long enough about the above example sentence, eventually they will probably figure out that we are talking about the two disjoint sets of the graph. However, to make things less confusing I would like to avoid a word like "part" which can mean so many different things in the English language.
We could use "disjoint sets" but the words "disjoint" and "set" won't be immediately familiar with the readers.
My current preferred term would be "partition" because when a country is partitioned, the average English speaker knows that "partition A" and "partition B" are the two disjoint partitions formed by the partitioning. However, for the very few people reading the paper that are trained in graph theory for example, would my use of the word "partition" be in-appropriate?
If so, what would be the alternatives to the word "part" that I can use?
graph-theory terminology word-problem bipartite-graph
asked Dec 2 at 20:20
user1271772
23518
add a comment |
up vote
2
down vote
favorite
Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example:
One "part" of the $K_{4,4}$ connects to a corresponding "part" of a
different graph while the other "part" does
not.
What are the synonyms (if any) that could be appropriate for replacing the word "part" here?
I am writing a paper for a very non-mathematical audience. This small community of researchers have come to learn what $K_{4,4}$ means, because it comes up often, but they have no other graph theory training and it will not be clear to them what "part" means. For example, the English word "part" could describe things like individual "vertices" or "edges". If the reader thinks long enough about the above example sentence, eventually they will probably figure out that we are talking about the two disjoint sets of the graph. However, to make things less confusing I would like to avoid a word like "part" which can mean so many different things in the English language.
We could use "disjoint sets" but the words "disjoint" and "set" won't be immediately familiar with the readers.
My current preferred term would be "partition" because when a country is partitioned, the average English speaker knows that "partition A" and "partition B" are the two disjoint partitions formed by the partitioning. However, for the very few people reading the paper that are trained in graph theory for example, would my use of the word "partition" be in-appropriate?
If so, what would be the alternatives to the word "part" that I can use?
graph-theory terminology word-problem bipartite-graph
asked Dec 2 at 20:20
user1271772
23518
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example:
One "part" of the $K_{4,4}$ connects to a corresponding "part" of a
different graph while the other "part" does
not.
What are the synonyms (if any) that could be appropriate for replacing the word "part" here?
I am writing a paper for a very non-mathematical audience. This small community of researchers have come to learn what $K_{4,4}$ means, because it comes up often, but they have no other graph theory training and it will not be clear to them what "part" means. For example, the English word "part" could describe things like individual "vertices" or "edges". If the reader thinks long enough about the above example sentence, eventually they will probably figure out that we are talking about the two disjoint sets of the graph. However, to make things less confusing I would like to avoid a word like "part" which can mean so many different things in the English language.
We could use "disjoint sets" but the words "disjoint" and "set" won't be immediately familiar with the readers.
My current preferred term would be "partition" because when a country is partitioned, the average English speaker knows that "partition A" and "partition B" are the two disjoint partitions formed by the partitioning. However, for the very few people reading the paper that are trained in graph theory for example, would my use of the word "partition" be in-appropriate?
If so, what would be the alternatives to the word "part" that I can use?
graph-theory terminology word-problem bipartite-graph
asked Dec 2 at 20:20
user1271772
23518
Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example:
One "part" of the $K_{4,4}$ connects to a corresponding "part" of a
different graph while the other "part" does
not.
What are the synonyms (if any) that could be appropriate for replacing the word "part" here?
I am writing a paper for a very non-mathematical audience. This small community of researchers have come to learn what $K_{4,4}$ means, because it comes up often, but they have no other graph theory training and it will not be clear to them what "part" means. For example, the English word "part" could describe things like individual "vertices" or "edges". If the reader thinks long enough about the above example sentence, eventually they will probably figure out that we are talking about the two disjoint sets of the graph. However, to make things less confusing I would like to avoid a word like "part" which can mean so many different things in the English language.
We could use "disjoint sets" but the words "disjoint" and "set" won't be immediately familiar with the readers.
My current preferred term would be "partition" because when a country is partitioned, the average English speaker knows that "partition A" and "partition B" are the two disjoint partitions formed by the partitioning. However, for the very few people reading the paper that are trained in graph theory for example, would my use of the word "partition" be in-appropriate?
If so, what would be the alternatives to the word "part" that I can use?
graph-theory terminology word-problem bipartite-graph
graph-theory terminology word-problem bipartite-graph
asked Dec 2 at 20:20
user1271772
23518
asked Dec 2 at 20:20
user1271772
23518
asked Dec 2 at 20:20
user1271772
23518
asked Dec 2 at 20:20
user1271772
23518
asked Dec 2 at 20:20
user1271772
23518
23518
add a comment |
add a comment |
1 Answer
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oldest
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up vote
2
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"Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A cup B$ with $A cap B = varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
|
show 2 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
"Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A cup B$ with $A cap B = varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
|
show 2 more comments
up vote
2
down vote
"Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A cup B$ with $A cap B = varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
|
show 2 more comments
up vote
2
down vote
up vote
2
down vote
"Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A cup B$ with $A cap B = varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
"Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A cup B$ with $A cap B = varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
edited Dec 2 at 20:51
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
answered Dec 2 at 20:38
Misha Lavrov
42.6k555101
42.6k555101
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
|
show 2 more comments
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(1) Yes this is what I was worried about, since "partition" means in some sense the "dividing line between A and B", not the "A" or "B" themselves. (2) "partite set" is good, but a bit too mathematical a term (partite for example is already underlined in read when I type it in Google Chrome, meaning it's not considered a word (3) I'd love to be able to say "Let G be a graph with parts A and B" but the readers will appreciate avoiding such mathematical definitions as much as possible (this would be hard to explain to a mathematician.. but it's just the way the readers think).
– user1271772
Dec 2 at 22:48
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
(4) I thought about "sides" too, but the classic left and right depiction of K4,4 is actually the worst one for our purposes... we prefer the diamond (where the "parts" go horizontal and vertical) or the triangle (think of K4,4 as lines between rows and columns of a matrix). (5) "Each part of the bipartition" might work best. However we'd have to say "Each part of the bipartition in K4,4" very often. Maybe the best thing to do is to define a term for the "parts" and then use that for the rest of the paper.
– user1271772
Dec 2 at 22:52
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
Defining a term is always a viable option, as long as it doesn't conflict with existing terminology.
– Misha Lavrov
Dec 2 at 22:57
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
I'm going to try that. It might be hard, but it's probably the best option. Unless someone else comes up with a term as ideal as "partition" would have been, if it didn't already have a mathematical meaning more specific than the general English meaning.
– user1271772
Dec 2 at 22:58
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
Colors might work well. You could say something like "$K_{4,4}$ is a graph with $4$ red vertices and $4$ blue vertices and an edge between every pair of vertices of different colors. We have a bunch of $K_{4,4}$'s and we connect a red vertex in one to a blue vertex in another under such and such conditions..."
– Misha Lavrov
Dec 2 at 23:00
|
show 2 more comments
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});
Sign up using Google
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Post as a guest
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Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
