## 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.

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 language | English |
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Pages (from-to) | 345-356 |

Number of pages | 12 |

Journal | Journal of Combinatorics |

Volume | 1 |

Issue number | 3-4 |

DOIs | |

State | Published - 2010 |