Improved algorithms for recognizing p-Helly and hereditary p-Helly hypergraphs

  • Authors:

  • Mitre C. Dourado;Min Chih Lin;Fábio Protti;Jayme L. Szwarcfiter

  • Affiliations:

  • Universidade Federal Rural do Rio de Janeiro, IC and UFRJ, NCE, Rio de Janeiro, RJ, Brazil;Universidad de Buenos Aires, DC, Buenos Aires, Argentina;Universidade Federal do Rio de Janeiro, IM and NCE, Rio de Janeiro, RJ, Brazil;Universidade Federal do Rio de Janeiro, IM, COPPE and NCE, Rio de Janeiro, RJ, Brazil

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

A hypergraph H is set of vertices V together with a collection of nonempty subsets of it, called the hyperedges of H. A partial hypergraph of H is a hypergraph whose hyperedges are all hyperedges of H, whereas for V^'@?V the subhypergraph (induced by V^') is a hypergraph with vertices V^' and having as hyperedges the subsets obtained as nonempty intersections of V^' and each of the hyperedges of H. For p=1 say that H is p-intersecting when every subset formed by p hyperedges of H contain a common vertex. Say that H is p-Helly when every p-intersecting partial hypergraph H^' of H contains a vertex belonging to all the hyperedges of H^'. A hypergraph is hereditary p-Helly when every (induced) subhypergraph of it is p-Helly. In this paper we describe new characterizations for hereditary p-Helly hypergraphs and discuss the recognition problems for both p-Helly and hereditary p-Helly hypergraphs. The proposed algorithms improve the complexity of the existing recognition algorithms.