| Full text | |
| Author(s): |
Allen, Peter
;
Bottcher, Julia
;
Cooley, Oliver
;
Mycroft, Richard
Total Authors: 4
|
| Document type: | Journal article |
| Source: | JOURNAL OF COMBINATORIAL THEORY SERIES A; v. 149, p. 30-100, JUL 2017. |
| Web of Science Citations: | 3 |
| Abstract | |
We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of the original hypergraph. Accordingly we advocate their use in extremal hypergraph theory, and explain how they can lead to considerable simplifications in existing proofs in this field. We also use them for establishing the following two new results. Firstly, we prove a hypergraph extension of the Erdos-Gallai Theorem: for every delta > 0 every sufficiently large k-uniform hypergraph with at least (alpha + delta)((eta)(kappa)) edges contains a tight cycle of length alpha eta for each alpha epsilon {[}0,1]. Secondly, we find (asymptotically) the minimum codegree requirement for a k-uniform k-partite hypergraph, each of whose parts has eta vertices, to contain a tight cycle of length alpha kappa eta, for each 0 < alpha < 1. (C) 2017 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 10/09555-7 - Embedding, randomised and structural problems in extremal graph theory |
| Grantee: | Peter David Allen |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 09/17831-7 - Embedding and packing problems in extremal graph theory |
| Grantee: | Julia Boettcher |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |