Article ID Journal Published Year Pages File Type
4650787 Discrete Mathematics 2008 5 Pages PDF
Abstract

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)|.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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