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Minimum codegree threshold for (K-4(3)-e)-factors
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 120, no 3, 708-721 p.Article in journal (Refereed) Published
Abstract [en]

Given hypergraphs H and F, an F-factor in H is a spanning subgraph consisting of vertex-disjoint copies of F. Let K-4(3) - e denote the 3-uniform hypergraph on 4 vertices with 3 edges. We Show that for any gamma > 0 there exists an integer n(0) such that every 3-uniform hypergraph H of order n > n(0) with minimum codegree at least (1/2 + gamma)n and 4 vertical bar n contains a (K-4(3) - e)-factor. Moreover, this bound is asymptotically the best possible and we further give a conjecture on the exact value of the threshold for the existence of a (K-4(3) - e)-factor. Thereby, all minimum codegree thresholds for the existence of F-factors are known asymptotically for 3-uniform hypergraphs F on 4 vertices. (C) 2012 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2013. Vol. 120, no 3, 708-721 p.
Keyword [en]
Hypergraph, 3-Graph, Factorization, Minimum codegree
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-66767DOI: 10.1016/j.jcta.2012.12.005ISI: 000314261100014OAI: oai:DiVA.org:umu-66767DiVA: diva2:611395
Available from: 2013-03-15 Created: 2013-03-05 Last updated: 2017-12-06Bibliographically approved

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Markström, Klas

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