Cyclic Matching Sequencibility of Graphs

TL;DR

This paper introduces the concept of cyclic matching sequencibility in graphs, establishing that for complete graphs with even and odd vertices, this value equals half the number of vertices minus one.

Contribution

The paper defines cyclic matching sequencibility and determines its exact value for complete graphs with both even and odd numbers of vertices.

Findings

Cyclic matching sequencibility of K_{2m} is m-1.

Cyclic matching sequencibility of K_{2m+1} is m-1.

Provides exact values for complete graphs.

Abstract

We define the cyclic matching sequencibility of a graph to be the largest integer $d$ such that there exists a cyclic ordering of its edges so that every $d$ consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of $K_{2m}$ and $K_{2m+1}$ equal $m-1$.