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, NOR. (Submitted)

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Abstract

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:	https://eurocomb2015.b.uib.no/
Additional Information:	© 2015 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	09 Dec 2015 14:34
Last Modified:	12 Dec 2024 04:56
URI:	http://eprints.lse.ac.uk/id/eprint/64638

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