The cyclic matching sequenceability of regular graphs

TL;DR

This paper investigates the cyclic matching sequenceability of regular graphs, providing exact results for 2-regular graphs and bounds for higher degrees, advancing understanding of edge orderings in graph theory.

Contribution

It determines the minimum cyclic matching sequenceability for 2-regular graphs and establishes bounds for k-regular graphs with k ≥ 3, offering new insights into graph edge arrangements.

Findings

Exact value for 2-regular graphs

Bounds for k-regular graphs with k ≥ 3

Enhanced understanding of cyclic edge orderings

Abstract

The cyclic matching sequenceability of a simple graph $G$, denoted $\mathrm{cms}(G)$, 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 $k \geq 3$.