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The density Turán problem for hypergraphs

Talbot, J; Sanitt, A; (2022) The density Turán problem for hypergraphs. Journal of Combinatorics (In press). Green open access

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Abstract

Given a k-graph H a complete blow-up of H is a k-graph Hˆ formed by replacing each v ∈ V (H) by a non-empty vertex class Av and then inserting all edges between any k vertex classes corresponding to an edge of H. Given a subgraph G ⊆ Hˆ and an edge e ∈ E(H) we define the density de(G) to be the proportion of edges present in G between the classes corresponding to e. The density Tur´an problem for H asks: determine the minimal value dcrit(H) such that any subgraph G ⊆ Hˆ satisfying de(G) > dcrit(H) for every e ∈ E(H) contains a copy of H as a transversal, i.e. a copy of H meeting each vertex class of Hˆ exactly once. We give upper bounds for this hypergraph density Tur´an problem that generalise the known bounds for the case of graphs due to Csikv´ari and Nagy [3], although our methods are different, employing an entropy compression argument.

Type: Article
Title: The density Turán problem for hypergraphs
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.intlpress.com/JOC/
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10138696
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