Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4650787 | Discrete Mathematics | 2008 | 5 Pages |
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
Authors
Graham A. Case, David A. Pike,