Coloring perfect graphs with no balanced skew-partitions

TL;DR

This paper introduces polynomial-time algorithms for finding maximum stable sets and coloring perfect graphs that lack balanced skew-partitions, improving computational methods for this class of graphs.

Contribution

It provides the first known polynomial algorithms for maximum stable set and coloring in perfect graphs without balanced skew-partitions.

Findings

Maximum stable set algorithm runs in O(n^5) time.

Graph coloring algorithm runs in O(n^7) time.

Algorithms are specifically designed for perfect graphs with no balanced skew-partitions.

Abstract

We present an $O(n^5)$ algorithm that computes a maximum stable set of any perfect graph with no balanced skew-partition. We present $O(n^7)$ time algorithm that colors them.