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Article Dans Une Revue Theoretical Computer Science Année : 2020

Efficient enumeration of maximal k-degenerate induced subgraphs of a chordal graph

Résumé

In this paper we consider the problem of listing the maximal k-degenerate induced subgraphs of a chordal graph, and propose an output-sensitive algorithm using delay for any n-vertex chordal graph with m edges, where is the maximum size of a clique in G. Degeneracy is a well known sparsity measure, and k-degenerate subgraphs are a notion of sparse subgraphs, which generalizes other problems such as independent sets (0-degenerate subgraphs) and forests (1-degenerate subgraphs). Many efficient enumeration algorithms are designed by solving the so-called Extension problem, which asks whether there exists a maximal solution containing a given set of nodes, but no node from a forbidden set. We show that solving this problem is np-complete for maximal k-degenerate induced subgraphs, motivating the need for additional techniques.
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Dates et versions

hal-04056387 , version 1 (03-04-2023)

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Alessio Conte, Mamadou Moustapha Kanté, Yota Otachi, Takeaki Uno, Kunihiro Wasa. Efficient enumeration of maximal k-degenerate induced subgraphs of a chordal graph. Theoretical Computer Science, 2020, 818, pp.2-11. ⟨10.1016/j.tcs.2018.08.009⟩. ⟨hal-04056387⟩
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