On the strong chromatic index and maximum induced matching of tree-cographs and permutation graphs

TL;DR

This paper presents linear-time algorithms for computing the strong chromatic index and maximum induced matching in tree-cographs, and an efficient algorithm for the same index in permutation graphs, advancing graph coloring and matching theory.

Contribution

It introduces new linear-time algorithms for key graph parameters in tree-cographs and permutation graphs, leveraging decomposition trees.

Findings

Linear-time algorithm for strong chromatic index of tree-cographs

Linear-time algorithm for maximum induced matching of tree-cographs

Efficient algorithm for strong chromatic index of permutation 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 exists an efficient algorithm for the strong chromatic index of permutation graphs.