A polynomial algorithm for the strong Helly property
نویسندگان
چکیده
In this article we give a polynomial algorithm to recognize if any partial sub hypergraph of a hypergraph has the Helly property
منابع مشابه
On the strong p-Helly property
The notion of strong p-Helly hypergraphs was introduced by Golumbic and Jamison in 1985 [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, J. Combin. Theory Ser. B 38 (1985) 8–22]. Independently, other authors [A. Bretto, S. Ubéda, J. Žerovnik, A polynomial algorithm for the strong Helly property. Inform. Process. Lett. 81 (2002) 55–57, E. Prisner, Hereditary clique-...
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In this article we characterize bipartite graphs whose associated neighborhood hypergraphs have the Helly property. We examine incidence graphs of both hypergraphs and linear hypergraphs and we give a polynomial algorithm to recognize if a linear hypergraph has the Helly property.
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We study the problem of satisfiability of Boolean formulas φ in conjunctive normal form whose literals have the form v ∈ S and express the membership of values to sets S of a given set system S. We establish the following dichotomy result. We show that checking the satisfiability of such formulas (called S-formulas) with three or more literals per clause is NP-complete except the trivial case w...
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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 classe...
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In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. A family of subsets has the Helly property when every subfamily thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations of this property exist which are relevant to some fields of mathematics, and have several applications in computer science. In this...
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 81 شماره
صفحات -
تاریخ انتشار 2002