Abstract
Letg(n,r) be the maximal order of an induced cycle in the Knesser graph Kn([n] r), whose vertices are ther-sets of [n]={1, ...,n} and whose adjacency relation is disjointness. Thusg(n, r) is the largestm for which there is a sequenceA 1,A 2,...,A m υ [n] ofr-sets withA i ∩A j=ϑ if and only if |i-j|=1 orm−1. We prove that there is an absolute constantc>0 for which
improving previous results. Our lower bound also shows that the clique covering number of the complement of ann-cycle is at most 1.459 log2 n for large enoughn. Related problems concerning the order of induced subgraphs of bounded degree of Kneser graphs are discussed.
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Research supported by FAPESP, Brazil, Proc. MAP 86/0904-8