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