1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Graph Theory

  1. Mar 25, 2010 #1
    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 n1/2



    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
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted