A note on Matching Cover Algorithm

TL;DR

This paper introduces an efficient $O(nm)$ algorithm for finding optimal matching covers in graphs, correcting a previous error in the existing algorithm and improving the computational approach.

Contribution

It presents a corrected and optimized algorithm for computing optimal matching covers in graphs, addressing errors in prior work.

Findings

Algorithm runs in $O(nm)$ time.

Corrects previous errors in matching cover algorithms.

Provides an efficient method for optimal matching cover computation.

Abstract

A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal matching cover of a graph on $n$ vertices and $m$ edges in $O(nm)$ time. This algorithm corrects an error of Matching Cover Algorithm in (Xiumei Wang, Xiaoxin Song, Jinjiang Yuan, On matching cover of graphs, Math. Program. Ser. A (2014)147: 499-518).