2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 273278
author:  Daniela Kühn and Deryk Osthus 

title:  Matchings and Hamilton cycles in hypergraphs 
keywords:  matchings, Hamilton cycles, packings, uniform hypergraphs 
abstract: 
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
ε> 0
there is an
n
such that every
0
3
uniform hypergraph of order
n ≥n
whose minimum degree is at least
0
n/4+εn
contains a Hamilton cycle. Our bounds on the minimum
degree are essentially best possible.

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reference:  Daniela Kühn and Deryk Osthus (2005), Matchings and Hamilton cycles in hypergraphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 273278 
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