Generalized octahedra and cliques in intersection graphs of uniform hypergraphs

Abstract It is shown that k -uniform hypergraphs with m edges contain at most O (m 2k k ) maximal sets of pairwise intersecting hyperedges, and l -intersection graphs G = (V,E) of k -uniform hypergraphs contain O (∣V∣ 2(k−l+1) k−l+1 ) maximal cliques. In case l = k−2 , the result is improved to O (∣V∣∣E∣) . For every fixed k , the results imply polynomial-time algorithms for computing maximum sets of pairwise intersecting hyperedges in k -uniform hypergraphs, respectively maximal cliques in their intersection graphs.