basic question on triangular maps in graph theory
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While doing the book "Probem Solving Strategies by Arthur Engel" I found this question:
"Can you draw a triangular map inside a pentagon, so that each vertex has an even degree?"
I know what degree of a vertex means, however I am not understanding what a triangular map means here? Also how do I solve this problem?
graph-theory
asked yesterday
saisanjeev
744212
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favorite
While doing the book "Probem Solving Strategies by Arthur Engel" I found this question:
"Can you draw a triangular map inside a pentagon, so that each vertex has an even degree?"
I know what degree of a vertex means, however I am not understanding what a triangular map means here? Also how do I solve this problem?
graph-theory
asked yesterday
saisanjeev
744212
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
While doing the book "Probem Solving Strategies by Arthur Engel" I found this question:
"Can you draw a triangular map inside a pentagon, so that each vertex has an even degree?"
I know what degree of a vertex means, however I am not understanding what a triangular map means here? Also how do I solve this problem?
graph-theory
asked yesterday
saisanjeev
744212
While doing the book "Probem Solving Strategies by Arthur Engel" I found this question:
"Can you draw a triangular map inside a pentagon, so that each vertex has an even degree?"
I know what degree of a vertex means, however I am not understanding what a triangular map means here? Also how do I solve this problem?
graph-theory
graph-theory
asked yesterday
saisanjeev
744212
asked yesterday
saisanjeev
744212
asked yesterday
saisanjeev
744212
asked yesterday
saisanjeev
744212
asked yesterday
saisanjeev
744212
744212
add a comment |
add a comment |
2 Answers
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You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).
This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.
answered yesterday
Vasily Mitch
1,05817
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
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A triangular map is a special case of a Regular map : https://en.wikipedia.org/wiki/Regular_map_(graph_theory)
answered yesterday
Florent Jousse
32
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).
This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.
answered yesterday
Vasily Mitch
1,05817
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
add a comment |
up vote
0
down vote
You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).
This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.
answered yesterday
Vasily Mitch
1,05817
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
add a comment |
up vote
0
down vote
up vote
0
down vote
You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).
This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.
answered yesterday
Vasily Mitch
1,05817
You can think of triangular map as of planar graph with all polygons that appear being topologically triangles (i.e. having 3 vertices and 3 edges).
This planar graph is not a triangular map because the face in the middle is quadrilateral. However, if you add diagonal to it, it becomes a triangular map.
answered yesterday
Vasily Mitch
1,05817
answered yesterday
Vasily Mitch
1,05817
answered yesterday
Vasily Mitch
1,05817
answered yesterday
Vasily Mitch
1,05817
1,05817
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
add a comment |
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Are you counting all the non overlapping polygons? And if we add the diagonal the quadrilateral will still exist right?
– saisanjeev
22 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
Yes, you are counting non-overlaping regions. As if the regions are countries and edges are borders between them. When you add diagonal, you split the quadrilateral country into two triangular ones.
– Vasily Mitch
18 hours ago
add a comment |
up vote
0
down vote
A triangular map is a special case of a Regular map : https://en.wikipedia.org/wiki/Regular_map_(graph_theory)
answered yesterday
Florent Jousse
32
add a comment |
up vote
0
down vote
A triangular map is a special case of a Regular map : https://en.wikipedia.org/wiki/Regular_map_(graph_theory)
answered yesterday
Florent Jousse
32
add a comment |
up vote
0
down vote
up vote
0
down vote
A triangular map is a special case of a Regular map : https://en.wikipedia.org/wiki/Regular_map_(graph_theory)
answered yesterday
Florent Jousse
32
A triangular map is a special case of a Regular map : https://en.wikipedia.org/wiki/Regular_map_(graph_theory)
answered yesterday
Florent Jousse
32
answered yesterday
Florent Jousse
32
answered yesterday
Florent Jousse
32
answered yesterday
Florent Jousse
32
32
add a comment |
add a comment |
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