### Algorithms for recognizing bipartite-Helly and bipartite-conformal hypergraphs,

A hypergraph is Helly if every family of hyperedges of it, formed by pairwise intersecting hyperedges, has a common vertex. We consider the concepts of bipartite-conformal and (colored) bipartite-Helly hypergraphs. In the same way as conformal hypergraphs and Helly hypergraphs are dual concepts, bipartite-conformal and bipartite-Helly hypergraphs are also dual. They are useful for characterizing biclique matrices and biclique graphs, that is, the...