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Math Help - Interval graph

  1. #1
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    Interval graph

    Prove that if G is a complement of an interval graph (http://en.wikipedia.org/wiki/Interval_graph):

    χ(G)=ω(G)
    where χ(G): chromatic number; ω(G): clique number

    Thank you in advance!
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  2. #2
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    We know that χ(G)>ω(G) is alwasys true for any graphs. So to prove the equality you just have to prove that χ(G)<=(G) is true as well. So you should admit that your graph is ω-colourable, it is enough to show an appropriate colouring using ω colours.
    It is useful to think over what a clique means in that G complement graph and which vertices are in the same colour class.
    clique: vertices that represents disjoint intervals
    vertices in the same colour class: they represents intervals that have a common point (have a common intersection)

    I hope that with the help of these hints you can solve the problem.
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  3. #3
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    Thanks a lot, but I am afraid I can't solve the problem.
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