Increasing the chromatic number of a random graph

Noga Alon, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

Abstract

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(n2/ log2 n) edges. We show that this is tight up to a constant factor, consider the question for more general random graphs Gn,p with p = p(n), and study a local version of the question
as well.
The question is motivated by the study of the resilience of graph properties, initiated by the second author and Vu, and improves one of their results.
Original languageEnglish
Pages (from-to)345-356
Number of pages12
JournalJournal of Combinatorics
Volume1
Issue number3-4
DOIs
StatePublished - 2010

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