How to color the verteces of triangles in different colors?
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I have a directed graph $G=(V_n, E)$, where $V_n ={1,2,..., n}$ is the set of vertices and $E$ is the set of edges.
I have found the set of triangles which looks like:
# A B C
1 7 21 24
2 8 10 13
3 2 8 13
4 14 19 25
5 18 20 24
6 20 21 24
7 7 20 21
8 7 20 24
9 5 20 24
Here $A$, $B$, $C$ are id's of the vertex in the $k$-th triangle.
I need to use a minimum number of colors to color the verticies of triangles in different colors.
My attempt is:
There are three situations for two triangles:
1) Triangles #1 (7,21,24) and #2 (8,10,13) don't have the common vertex and I can use two colors.
2) Triangles #5 (18,20,24) and #7 (7,20,21) have the common vertex 20 and I can use two colors.
3) Triangles #7 (7,20,21) and #8 (7,20,24) have the two common vertices 7, 20 and I can use two colors.
Question. Which is an algorithm one can use to solve this vertex coloring task?
Edit. The close task on the edge's set is here https://stackoverflow.com/questions/40432322/color-each-edge-in-triangle-igraph
graph-theory algorithms coloring
asked Nov 24 at 9:14
Nick
301112
add a comment |
up vote
1
down vote
favorite
I have a directed graph $G=(V_n, E)$, where $V_n ={1,2,..., n}$ is the set of vertices and $E$ is the set of edges.
I have found the set of triangles which looks like:
# A B C
1 7 21 24
2 8 10 13
3 2 8 13
4 14 19 25
5 18 20 24
6 20 21 24
7 7 20 21
8 7 20 24
9 5 20 24
Here $A$, $B$, $C$ are id's of the vertex in the $k$-th triangle.
I need to use a minimum number of colors to color the verticies of triangles in different colors.
My attempt is:
There are three situations for two triangles:
1) Triangles #1 (7,21,24) and #2 (8,10,13) don't have the common vertex and I can use two colors.
2) Triangles #5 (18,20,24) and #7 (7,20,21) have the common vertex 20 and I can use two colors.
3) Triangles #7 (7,20,21) and #8 (7,20,24) have the two common vertices 7, 20 and I can use two colors.
Question. Which is an algorithm one can use to solve this vertex coloring task?
Edit. The close task on the edge's set is here https://stackoverflow.com/questions/40432322/color-each-edge-in-triangle-igraph
graph-theory algorithms coloring
asked Nov 24 at 9:14
Nick
301112
Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have a directed graph $G=(V_n, E)$, where $V_n ={1,2,..., n}$ is the set of vertices and $E$ is the set of edges.
I have found the set of triangles which looks like:
# A B C
1 7 21 24
2 8 10 13
3 2 8 13
4 14 19 25
5 18 20 24
6 20 21 24
7 7 20 21
8 7 20 24
9 5 20 24
Here $A$, $B$, $C$ are id's of the vertex in the $k$-th triangle.
I need to use a minimum number of colors to color the verticies of triangles in different colors.
My attempt is:
There are three situations for two triangles:
1) Triangles #1 (7,21,24) and #2 (8,10,13) don't have the common vertex and I can use two colors.
2) Triangles #5 (18,20,24) and #7 (7,20,21) have the common vertex 20 and I can use two colors.
3) Triangles #7 (7,20,21) and #8 (7,20,24) have the two common vertices 7, 20 and I can use two colors.
Question. Which is an algorithm one can use to solve this vertex coloring task?
Edit. The close task on the edge's set is here https://stackoverflow.com/questions/40432322/color-each-edge-in-triangle-igraph
graph-theory algorithms coloring
asked Nov 24 at 9:14
Nick
301112
I have a directed graph $G=(V_n, E)$, where $V_n ={1,2,..., n}$ is the set of vertices and $E$ is the set of edges.
I have found the set of triangles which looks like:
# A B C
1 7 21 24
2 8 10 13
3 2 8 13
4 14 19 25
5 18 20 24
6 20 21 24
7 7 20 21
8 7 20 24
9 5 20 24
Here $A$, $B$, $C$ are id's of the vertex in the $k$-th triangle.
I need to use a minimum number of colors to color the verticies of triangles in different colors.
My attempt is:
There are three situations for two triangles:
1) Triangles #1 (7,21,24) and #2 (8,10,13) don't have the common vertex and I can use two colors.
2) Triangles #5 (18,20,24) and #7 (7,20,21) have the common vertex 20 and I can use two colors.
3) Triangles #7 (7,20,21) and #8 (7,20,24) have the two common vertices 7, 20 and I can use two colors.
Question. Which is an algorithm one can use to solve this vertex coloring task?
Edit. The close task on the edge's set is here https://stackoverflow.com/questions/40432322/color-each-edge-in-triangle-igraph
graph-theory algorithms coloring
graph-theory algorithms coloring
asked Nov 24 at 9:14
Nick
301112
asked Nov 24 at 9:14
Nick
301112
edited Nov 24 at 10:50
asked Nov 24 at 9:14
Nick
301112
asked Nov 24 at 9:14
Nick
301112
asked Nov 24 at 9:14
Nick
301112
301112
Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41
add a comment |
Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41
Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41
add a comment |
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Your problem statement is very unclear. What does it mean to "color the triangles in different colors"? Do you have to assign colours to vertices or to triangles? And why can't you colour everything with the same colour?
– Rahul
Nov 24 at 9:26
@rahul, i what to assign the set of colours to vertices, unfortunatlly, i can not found the name of this task.
– Nick
Nov 24 at 9:41