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Increasing the chromatic number of a random graph

2010
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Journal of Combinatorics
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What is the minimum number of edges that have to be added to the random graph G = G n,0.5 in order to increase its chromatic number χ = χ(G) by one percent ? One possibility is to add all missing edges on a set of 1.01χ vertices, thus creating a clique of chromatic number 1.01χ. This requires, with high probability, the addition of Ω(n 2 / log 2 n) edges. We show that this is tight up to a constant factor, consider the question for more general random graphs G n,p with p = p(n), and study a

doi:10.4310/joc.2010.v1.n4.a1
fatcat:wpcufocnirdhhpf3vzayk3ofde