Isomorphic edge disjoint subgraphs of hypergraphs1. Issue 4 (12th February 2016) - Horn, Paul; Koubek, Václav; Rödl, Vojtěch
Abstract: We show that any k ‐uniform hypergraph with n edges contains two isomorphic edge disjoint subgraphs of size Ω ˜ ( n 2 / ( k + 1 ) ) for k = 4, 5 and 6. This is best possible up to a logarithmic factor due to an upper bound construction of Erdős, Pach, and Pyber who show there exist k ‐uniform hypergraphs with n edges and with no two edge disjoint isomorphic subgraphs with size larger than O ˜ ( n 2 / ( k + 1 ) ) . Furthermore, our result extends results Erdős, Pach and Pyber who also established the lower bound for k = 2 (eg. for graphs), and of Gould and Rödl who established the result for k = 3. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 767–793, 2016