Daniela Kühn ; Deryk Osthus - Matchings and Hamilton cycles in hypergraphs

dmtcs:3457 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3457
Matchings and Hamilton cycles in hypergraphsArticle

Authors: Daniela Kühn 1; Deryk Osthus 1

  • 1 School of Mathematics [Birmingham]

It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on Hamilton cycles for $3$-uniform hypergraphs: We say that a $3$-uniform hypergraph has a Hamilton cycle if there is a cyclic ordering of its vertices such that every pair of consecutive vertices lies in a hyperedge which consists of three consecutive vertices. We prove that for every $\varepsilon > 0$ there is an $n_0$ such that every $3$-uniform hypergraph of order $n \geq n_0$ whose minimum degree is at least $n/4+ \varepsilon n$ contains a Hamilton cycle. Our bounds on the minimum degree are essentially best possible.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: matchings,Hamilton cycles,packings,uniform hypergraphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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