The helly property on subfamilies of limited size

Authors:
Mitre C. Dourado;Fábio Protti;Jayme L. Szwarcfiter
Affiliations:
UFRJ-COPPE, Rio de Janeiro, RJ, Brasil;Universidade Federal do Rio de Janeiro, Instituto de Matemática and NCE, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brasil;Universidade Federal do Rio de Janeiro, Instituto de Matemática, NCE and COPPE, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brasil
Venue:
Information Processing Letters
Year:
2005

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Abstract

In this work we consider the problem of determining whether a hypergraph has the p-Helly property, when the considered subfamilies are limited by a size k. That is, whether every partial hypergraph with at most k edges is p-Helly. Further, we study the related problem applied to the cliques of a graph. In all cases, depending on the values of p and k, either we show that the problem can be solved in polynomial time, or we describe a NP-hardness proof.