Convex Independence in Permutation Graphs

TL;DR

This paper investigates convex independence in permutation graphs, showing that the maximum size of such sets can be efficiently computed, advancing understanding of graph convexity properties.

Contribution

It establishes that the maximum size of convexly independent sets in permutation graphs can be determined in polynomial time, a novel computational result.

Findings

Maximum convexly independent sets can be computed in polynomial time.

Convex independence relates to P_3-convexity in permutation graphs.

The paper provides algorithms for identifying these sets.

Abstract

A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest P_3-convex set that contains A. A set M is convexly independent if for every vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time.