Linear Time Recognition of Equimatchable Split Graphs

TL;DR

This paper presents a linear time algorithm to recognize equimatchable split graphs, a class of graphs where all maximal matchings have the same size and vertices can be partitioned into a clique and an independent set.

Contribution

The paper introduces the first linear time recognition algorithm for equimatchable split graphs, combining properties of split graphs and equimatchability.

Findings

Linear time recognition algorithm for equimatchable split graphs

Characterization of equimatchable split graphs

Efficient graph classification method

Abstract

A maximal matching $M$ that consists of independent edges is a subgraph of a simple and undirected graph $G$ for which $G-M$ forms an independent set. A graph $G$ is called equimatchable if all maximal matchings have the same number of edges. On the other hand, $G$ is called as a split graph if its vertices can be partitioned into two subsets for which one of them forms a clique whereas the second forms an independent set. We will give a linear time algorithm for recognition of equimatchable split graphs.