Isomorphic Edge Disjoint Subgraphs of Hypergraphs
College of Natural Science and Mathematics, Mathematics
Subgraphs, Isomorphisms, Self‐similarity, Uniform hypergraphs
We show that any k‐uniform hypergraph with n edges contains two isomorphic edge disjoint subgraphs of size 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 . 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.
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Horn, Paul, et al. “Isomorphic Edge Disjoint Subgraphs of Hypergraphs.” Random Structures & Algorithms, vol. 48, no. 4, 2016, pp. 767–793. doi: 10.1002/rsa.20635.