Pancyclic PBD block-intersection graphs

Given a combinatorial design DD with block set BB, its block-intersection graph GDGD is the graph having vertex set BB such that two vertices b1b1 and b2b2 are adjacent if and only if b1b1 and b2b2 have non-empty intersection. In this paper, we prove that if DD is a pairwise balanced design, PBD(v,K,λ)(v,K,λ), with arbitrary index λ⩾1λ⩾1 and maxK⩽λminKmaxK⩽λminK, then GDGD contains a cycle of each length ℓ=3,4,…,|V(GD)|ℓ=3,4,…,|V(GD)|.