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Help Needed: Graph Theory Assignment on Vertex Colouring
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[QUOTE="ak_89, post: 2641697, member: 237586"] I am working on graph theory assignment. I need help because I am not seeing where I am going with this question. Here's the question: G is a simple graph with n vertices. -> show that vertex colouring of G [ X(G) ]* vertex colouring of G complement >= n -> show that the vertex colouring of G + the vertex colouring of G complement >= 2 n[SUP]1/2[/SUP] Here's what I have looked at. I know Chi (G) =< [tex]\Delta G +1[/tex] and same with G complement. [tex]\Delta G[/tex] =< n-1. Then I kind of played around with it. Didn't get anywhere. Then I tried again. I know Chi (X) >= n/[tex]\alpha (G)[/tex] and Chi (X) >= [tex]\omega (G complement)[/tex] = [tex]\alpha (G)[/tex] So I know Chi(G) >= [tex]\alpha (G complement) [/tex] and Chi(G complement) >=[tex]\alpha (G) [/tex] and Now I am totally confused... not sure what to do. If I could get some help that would be great. Thanks [/QUOTE]
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Help Needed: Graph Theory Assignment on Vertex Colouring
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