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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2008

On hereditary Helly classes of graphs

Abstract

In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of clique-Helly, disk-Helly, biclique-Helly, neighbourhood-Helly graphs, respectively. A natural question is to determine for which graphs the corresponding Helly property holds, for every induced subgraph. This leads to the corresponding classes of hereditary clique-Helly, hereditary disk-Helly, hereditary biclique-Helly and hereditary neighbourhood-Helly graphs. In this paper, we describe characterizations in terms of families of forbidden subgraphs, for the classes of hereditary biclique-Helly and hereditary neighbourhood-Helly graphs. We consider both open and closed neighbourhoods. The forbidden subgraphs are all of fixed size, implying polynomial time recognition for these classes.
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Dates and versions

hal-00972306 , version 1 (03-04-2014)

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Marina Groshaus, Jayme Luiz Szwarcfiter. On hereditary Helly classes of graphs. Discrete Mathematics and Theoretical Computer Science, 2008, Vol. 10 no. 1 (1), pp.71--78. ⟨10.46298/dmtcs.440⟩. ⟨hal-00972306⟩

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