Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 703.05044
Autor: Erdös, Paul; Pach, János; Pyber, L.
Title: Isomorphic subgraphs in a graph. (In English)
Source: Combinatorics, Proc. 7th Hung. Colloq., Eger/Hung. 1987, Colloq. Math. Soc. János Bolyai 52, 553-556 (1988).
Review: [For the entire collection see Zbl 673.00009.]
Let fr,s(n) denote the maximum integer f such that every r-uniform hypergraph H of size n contains s pairwise edge-disjoint isomorphic subhypergraphs of size f each. The authors prove that for every r \geq 3 and s \geq 2 there exist constants cr,s, dr,s > 0 such that cr,sns/(rs-1) < fr,s(n) < dr,sns/(rs-r+1)· \frac{log n}{log log n}. The particularization to graphs (r = 2) settles a problem posed by Schönheim.
Reviewer: K.R.Parthasarathy
Classif.: * 05C65 Hypergraphs
05C70 Factorization, etc.
05C60 Isomorphism problems (graph theory)
Keywords: partition; uniform hypergraph
Citations: Zbl 673.00009
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