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Tight cycles in hypergraphs

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Cooley, Oliver and Mycroft, Richard (2015) Tight cycles in hypergraphs. In: European Conference on Combinatorics, Graph Theory and Applications, 2015-08-31 - 2015-09-04, Bergen, Norway. (Submitted)

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We apply a recent version of the Strong Hypergraph Regularity Lemma(see [1], [2]) to prove two new results on tight cycles in k-uniform hypergraphs. The first result is an extension of the Erdos-Gallai Theorem for graphs: For every > 0, every sufficiently large k-uniform hypergraph on n vertices with at least edges contains a tight cycle of length @n for any @ 2 [0; 1]. Our second result concerns k-partite k-uniform hypergraphs with partition classes of size n and for each @ 2 (0; 1) provides an asymptotically optimal minimum codegree requirement for the hypergraph to contain a cycle of length @kn.

Item Type: Conference or Workshop Item (Paper)
Official URL:
Additional Information: © 2015 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 09 Dec 2015 14:34
Last Modified: 01 Nov 2021 00:11

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