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A hypermap is bipartite if its set of flags can be divided into two parts Aand B so that both A and B are the union of vertices, and consecutive verticesaround an edge or a face are contained in alternate parts. A bipartite hypermapis bipartite-regular if its set of automorphisms is transitive on A and on B.  In this paper we see some properties of the constructions of bipartitehypermaps described algebraically by Breda and Duarte which generalize theconstruction induced by the Walsh representation of hypermaps. As anapplication we show that all surfaces have bipartite-regular hypermaps.

Constructions of bipartite and bipartite-regular hypermaps