Title

Complete r-partite subgraphs of dense r-graphs

Abstract

Extending a classical result of Erdo{double acute}s, we derive the following concise statement:. Let r ≥ 3 and (ln n)- 1 / (r - 1) ≤ α ≤ r- 3. Then every r-uniform graph on n vertices with at least α nr / r ! edges contains a complete r-partite subgraph with r - 1 classes of size ⌊ α (ln n)1 / (r - 1) ⌋ and one class of size ⌈ n1 - αr - 2 ⌉. Our main result is a similar, but stronger statement about directed hypergraphs. © 2009 Elsevier B.V. All rights reserved.

Publication Title

Discrete Mathematics

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