k-Probe DH-graphs

TL;DR

This paper introduces a polynomial-time algorithm to determine whether a given graph can be embedded into a distance hereditary graph by adding edges within k independent sets, generalizing the concept of probe graphs.

Contribution

It defines k-probe distance hereditary graphs and provides an efficient algorithm to recognize them, extending the class of probe graphs.

Findings

Polynomial-time recognition algorithm for k-probe DH-graphs

Generalization of probe graph concept to distance hereditary graphs

Efficient embedding verification process

Abstract

Let k be a natural number. Let G be a graph and let N_1,...,N_k be k independent sets in G. The graph G is k-probe distance hereditary if G can be embedded into a DH-graph by adding edges between vertices that are contained in the same independent set. We show that there exists a polynomial-time algorithm to check if a graph G is k-probe distance hereditary.