Title

The girth of a design

Document Type

Article

Publication Date

2002

Publication Title

Journal of Combinatorial Mathematics and Combinatorial Computing

Department

Mathematics and Computer Science

Abstract

In 1976 Erdös asked about the existence of Steiner triple systems that lack collections of j blocks employing just j + 2 points. This has led to the study of anti-Pasch, anti-mitre and 5-sparse Steiner triple systems. Simultaneously generating sets and bases for Steiner triple systems and t-designs have been determined. Combining these ideas, together with the observation that a regular graph is a 1-design, we arrive at a natural definition for the girth of a design. In turn, this provides a natural extension of the search for cages to the universe of all t-designs. We include the results of computational experiments that give an abundance of examples of these new definitions.

Volume

40

pp.

97-113

ISSN

0835-3026