Bipartite bihypergraphs: A survey and new results

Inna Zverovich, Igor Zverovich
2006 Discrete Mathematics  
Let H 0 and H 1 be hypergraphs with the same vertex-set V . The ordered pair In Section 1, we survey numerous applications of bipartite bihypergraphs. In Section 3, we show that recognizing bipartite bihypergraphs within classes of k-complete bihypergraphs can be done in polynomial time. A bihypergraph H = (H 0 , H 1 ) is called k-complete, k 0, if each k-subset of V (H ) contains a hyperedge of H, i.e., a hyperedge of H 0 or H 1 . Moreover, we can construct all bipartitions of a k-complete
more » ... pergraph, if any, in polynomial time. A bihypergraph H = (H 0 , H 1 ) is called strongly bipartite if each maximal stable set of H 0 is a transversal of H 1 . We show that recognizing strongly bipartite bihypergraphs (H 0 , H 1 ) is a co-NP-complete problem even in the case where H 0 is a graph and H 1 has exactly one hyperedge. Some examples of strongly bipartite bihypergraphs are given.
doi:10.1016/j.disc.2005.10.026 fatcat:aszv3zjsufa53lilud5yq2j3ci