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 pairwise balanced design, PBD ( v , K , λ ) , with arbitrary index λ ⩾ 1 and max K ⩽ λ min K , then G D contains a cycle of each length ℓ = 3 , 4 , … , | V ( G D ) | .
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