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
Recommended Citation
Nikiforov, V. (2009). Complete r-partite subgraphs of dense r-graphs. Discrete Mathematics, 309 (13), 4326-4331. https://doi.org/10.1016/j.disc.2009.01.008
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