Pancyclic BIBD block-intersection graphs Original Research Article

Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 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 GD contains a cycle of each length ℓ=3,4,…,|V(GD)|.