A note on probe cographs

TL;DR

This paper introduces an algorithm to determine whether a given graph can be embedded into a cograph by adding edges within specific independent sets, extending the understanding of probe cographs.

Contribution

The paper presents an O(k n^5) algorithm for recognizing k-probe cographs, providing a computational method for this class of graphs.

Findings

Algorithm runs in polynomial time O(k n^5)

Recognition of k-probe cographs is computationally feasible

Extends the theory of probe cographs with an efficient recognition method

Abstract

Let G be a graph and let N_1, ..., N_k be k independent sets in G. The graph G is a k-probe cograph if G can be embedded into a cograph by adding edges between vertices that are contained in the same independent set. We show that there exists an O(k n^5) algorithm to check if a graph G is a k-probe cograph.