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Loose Hamilton Cycles in Regular Hypergraphs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 24, no 1, 179-194 p.Article in journal (Refereed) Published
Abstract [en]

We establish a relation between two uniform models of random k-graphs (for constant k >= 3) on n labelled vertices: H-(k)(n, m), the random k-graph with exactly m edges, and H-(k)(n, d), the random d-regular k-graph. By extending the switching technique of McKay and Wormald to k-graphs, we show that, for some range of d = d(n) and a constant c > 0, if m similar to cnd, then one can couple H-(k)(n, m) and H-(k)(n, d) so that the latter contains the former with probability tending to one as n -> infinity. In view of known results on the existence of a loose Hamilton cycle in H-(k)(n, m), we conclude that H-(k)(n, d) contains a loose Hamilton cycle when d >> log n (or just d >= C log n, if k = 3) and d = o(n(1/ 2)).

Place, publisher, year, edition, pages
2015. Vol. 24, no 1, 179-194 p.
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URN: urn:nbn:se:uu:diva-246665DOI: 10.1017/S0963548314000406ISI: 000348381100005OAI: oai:DiVA.org:uu-246665DiVA: diva2:796115
Available from: 2015-03-18 Created: 2015-03-09 Last updated: 2016-02-17Bibliographically approved

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