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On random subgraphs of Kneser and Schrijver graphs
[article]

2015
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arXiv
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pre-print

A Kneser graph KG_n,k is a graph whose vertices are in one-to-one correspondence with k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lovász states that the chromatic number of a Kneser graph KG_n,k is equal to n-2k+2. In this paper we study the chromatic number of a random subgraph of a Kneser graph KG_n,k as n grows. A random subgraph KG_n,k(p) is obtained by including each edge of KG_n,k with probability p.

arXiv:1502.00699v2
fatcat:jfjwzkjjebdejoye75qvqedlqe