Abstract
A cycle transversal or feedback vertex set of a graph G is a subset T⊆V(G) such that T∩V(C)≠0̸ for every cycle C 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.
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