Triangle-free Hamiltonian Kneser graphs

Authors:
Ya-Chen Chen
Affiliations:
Department of Mathematics, Arizona State University, P.O. Box 871804, Tempe, AZ
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

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Abstract

The Kneser graph K(n,k) has as vertices the k-subsets of {1, 2,...,n}. Two vertices are adjacent if the k-sets are disjoint. When n 3k, the Kneser Graph K(n, k) has no triangle. In this paper, we prove that K(n,k) is Hamiltonian for n ≥ (3k + 1 + √5k2- 2k + 1)/2, and extend this to the bipartite Kneser graphs. Note that (3k + 1 + √5k2 - 2k + 1)/2 2.62k + 1.