A question about graph coloring and partition of graph
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I got this question from professor, any hint would be helpful.
Let $k$ be a positive integer and let $X,Y$ be a partition of the vertex set of the graph $G$ such that $chi(G[X])le k$ and $chi(G[Y])le k$.
Suppose $e(X,Y)le k-1$. Then $chi(G)le k$.
graph-theory coloring
asked Nov 19 at 21:53
maskliesink
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add a comment |
up vote
0
down vote
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I got this question from professor, any hint would be helpful.
Let $k$ be a positive integer and let $X,Y$ be a partition of the vertex set of the graph $G$ such that $chi(G[X])le k$ and $chi(G[Y])le k$.
Suppose $e(X,Y)le k-1$. Then $chi(G)le k$.
graph-theory coloring
asked Nov 19 at 21:53
maskliesink
11
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I got this question from professor, any hint would be helpful.
Let $k$ be a positive integer and let $X,Y$ be a partition of the vertex set of the graph $G$ such that $chi(G[X])le k$ and $chi(G[Y])le k$.
Suppose $e(X,Y)le k-1$. Then $chi(G)le k$.
graph-theory coloring
asked Nov 19 at 21:53
maskliesink
11
I got this question from professor, any hint would be helpful.
Let $k$ be a positive integer and let $X,Y$ be a partition of the vertex set of the graph $G$ such that $chi(G[X])le k$ and $chi(G[Y])le k$.
Suppose $e(X,Y)le k-1$. Then $chi(G)le k$.
graph-theory coloring
graph-theory coloring
asked Nov 19 at 21:53
maskliesink
11
asked Nov 19 at 21:53
maskliesink
11
asked Nov 19 at 21:53
maskliesink
11
asked Nov 19 at 21:53
maskliesink
11
asked Nov 19 at 21:53
maskliesink
11
11
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11
add a comment |
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11
add a comment |
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Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Nov 19 at 21:57
My question when trying to answer your question: math.stackexchange.com/questions/3005657/…
– mathnoob
Nov 19 at 23:11