On the strong chromatic index and induced matching of tree-cographs, permutation graphs and chordal bipartite graphs

TL;DR

This paper presents linear-time algorithms for computing the strong chromatic index and maximum induced matching in tree-cographs, permutation graphs, and chordal bipartite graphs, enhancing efficiency in graph coloring problems.

Contribution

It introduces new efficient algorithms for key graph parameters in specific graph classes, leveraging decomposition trees and structural properties.

Findings

Linear-time algorithms for tree-cographs with decomposition trees.

Efficient algorithms for permutation graphs.

Algorithms for chordal bipartite graphs.

Abstract

We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exist efficient algorithms for the strong chromatic index of (bipartite) permutation graphs and of chordal bipartite graphs.