Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653882 | European Journal of Combinatorics | 2012 | 7 Pages |
Abstract
The definition of the Helly property for hypergraphs was motivated by the Helly theorem for convex sets. Similarly, we define the colorful Helly property for a family of hypergraphs, motivated by the colorful Helly theorem for collections of convex sets, by Lovász. We describe some general facts about the colorful Helly property and prove complexity results. In particular, we show that it is Co-NP-complete to decide if a family of p hypergraphs is colorful Helly, even if p=2. However, for any fixed p, we describe a polynomial time algorithm to decide if such family is colorful Helly, provided at least pâ1 of the hypergraphs are p-Helly.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Rommel M. Barbosa, Erika M.M. Coelho, Mitre C. Dourado, Jayme L. Szwarcfiter,