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

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

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

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

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 determine… Expand

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

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