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Distance-hereditary graphs are clique-perfect. (English) Zbl 1110.68108
Summary: We show that the clique-transversal number \(\tau_C(G)\) and the clique-independence number \(\alpha_C(G)\) are equal for any distance-hereditary graph \(G\). As a byproduct of proving that \(\tau_C(G)= \alpha_C(G)\), we give a linear-time algorithm to find a minimum clique-transversal set and a maximum clique-independent set simultaneously for distance-hereditary graphs.
Reviewer: Reviewer (Berlin)

68R10 Graph theory (including graph drawing) in computer science
05C12 Distance in graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C85 Graph algorithms (graph-theoretic aspects)
Full Text: DOI
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