Pancyclic BIBD block-intersection graphs

Abstract

Given a combinatorial design D with block set B , its block-intersection graph G D is the graph having vertex set B such that two vertices b 1 and b 2 are adjacent if and only if b 1 and b 2 have non-empty intersection. In this paper, we prove that if D is a balanced incomplete block design, BIBD( v, k, λ), with arbitrary index λ, then G D contains a cycle of each length ℓ=3,4,…,|V(G D )| .