The cyclic matching sequenceability of regular graphs

Abstract

The cyclic matching sequenceability of a simple graph G, denoted cms(G), is the largest integer s for which there exists a cyclic ordering of the edges of G so that every set of s consecutive edges forms a matching. In this paper we consider the minimum cyclic matching sequenceability of k-regular graphs. We completely determine this for 2-regular graphs, and give bounds for k 3.