Increasing the chromatic number of a random graph

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Increasing the chromatic number of a random graph

What is the minimum number of edges that have to be added to the random graph G = Gn,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/ log n) edges. We show that this is tight up to a constant f...

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ژورنال

عنوان ژورنال: Journal of Combinatorics

سال: 2010

ISSN: 2156-3527,2150-959X

DOI: 10.4310/joc.2010.v1.n4.a1