On isomorphic subgraphs

Gould, R.J. and V. RodI, On isomorphic subgraphs, Discrete Mathematics 118 (1993) 2599262. We prove that every 3-uniform hypergraph with 4 edges contain two edge disjoint isomorphic subgraphs with at least L&A J edges, This answers a question of Erdiis, Path and Pyber. Recently, the following question was independently raised by MS. Jacobson (personal communication) and J. Schonheim (see Cl]). In an arbitrary graph or hypergraph G, what is the maximum possible s such that G contains a pair of edge disjoint isomorphic subgraphs of size s? Erdiis et al. [l] provided bounds on the maximum size of such isomorphic subgraphs for graphs and hypergraphs. Let fk(q) denote the maximum integer such that in every graph (k = 2) or k-uniform hypergraph (k 3 3) of size q, one can find a pair of edge disjoin isomorphic subgraphs of size fk(q). In [l] it is shown that there exist constants cr and c2 (that depend only on k) such that