Clique cycle-transversals in distance-hereditary graphs

TL;DR

This paper characterizes distance-hereditary graphs that admit a clique cycle-transversal by identifying forbidden induced subgraphs, extending known results from chordal graphs and cographs.

Contribution

It provides a structural characterization of distance-hereditary graphs with a clique cycle-transversal through forbidden subgraph conditions.

Findings

Characterization of distance-hereditary graphs with cct

Extension of results from chordal graphs and cographs

Identification of forbidden induced subgraphs

Abstract

A cycle-transversal of a graph G is a subset T of V(G) such that T intersects every cycle of G. A clique cycle-transversal, or cct for short, is a cycle-transversal which is a clique. Recognizing graphs which admit a cct can be done in polynomial time; however, no structural characterization of such graphs is known. We characterize distance-hereditary graphs admitting a cct in terms of forbidden induced subgraphs. This extends similar results for chordal graphs and cographs.