An O(n) Time Algorithm For Maximum Induced Matching In Bipartite Star_123-free Graphs

TL;DR

This paper introduces a simple and efficient O(n) time algorithm for finding maximum induced matchings in bipartite Star_123-free graphs, improving upon previous algorithms with higher complexity.

Contribution

The paper presents the first linear-time algorithm for maximum induced matching in bipartite Star_123-free graphs, generalizing and improving previous results.

Findings

The algorithm runs in O(n) time.

It effectively solves the maximum induced matching problem in the specified graph class.

The approach simplifies previous methods and enhances computational efficiency.

Abstract

A matching in a graph is a set of edges no two of which share a common vertex. A matching M is an induced matching if no edge connects two edges of M. The problem of finding a maximum induced matching is known to be NP-hard in general and specifically for bipartite graphs. Lozin has been proposed an O(n^3) time algorithm for this problem on the class of bipartite Star_123,Sun_4-free graphs. In this paper we improve and generalize this result in presenting a simple O(n) time algorithm for maximum induced matching problem in bipartite Star_123-free graphs.