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The minimum degree threshold for perfect graph packings
TLDR
We determine up to an additive constant the minimum degree of a graph G which ensures that G has a perfect H-packing (also called an H-factor). Expand
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Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments
TLDR
A long-standing conjecture of Kelly states that every regular tournament on n vertices can be decomposed into edge-disjoint Hamilton cycles. Expand
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Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
  • D. Kühn, D. Osthus
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 November 2006
TLDR
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. Expand
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Popularity based random graph models leading to a scale-free degree sequence
TLDR
We introduce the following random graph model, which generalizes an earlier model of Barabasi and Albert (Science 286 (1999) 509) for the growth of the world wide web. Expand
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On Pósa's Conjecture for Random Graphs
TLDR
We prove that if $p \ge n^{-1/2+\varepsilon}$, then asymptotically almost surely, the binomial random graph $G_{n,p contains the square of a Hamilton cycle. Expand
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Edge-decompositions of graphs with high minimum degree
TLDR
A fundamental theorem of Wilson states that, for every graph $F$, every sufficiently large $F$-divisible graph of minimum degree at least $9n/10+o(n)$ has a $K_3$-decomposition. Expand
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Matchings in 3-uniform hypergraphs
TLDR
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. Expand
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Critical chromatic number and the complexity of perfect packings in graphs
Let <i>H</i> be any non-bipartite graph. We determine asymptotically the minimum degree of a graph <i>G</i> which ensures that <i>G</i> has a perfect <i>H</i>-packing. More precisely, we determineExpand
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An exact minimum degree condition for Hamilton cycles in oriented graphs
We show that every sufficiently large oriented graph G with +(G), �(G)(3n�4)/8 contains a Hamilton cycle. This is best possible and solves a problem of Thomassen from 1979
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Hamiltonian degree sequences in digraphs
TLDR
We show that for each @h>0 every digraph G of sufficiently large order n is Hamiltonian if its out- and indegree sequences d"1^+= =n-i and (ii) d"i^->=i+@hn or d"n"-"i"-"@h"n^+>=n-I for all i . Expand
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