Let H be a k-graph on n vertices, with minimum codegree at least n/k + cn for some fixed c > 0. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H or aâ€¦ (More)

We show that if pn log n the binomial random graph Gn,p has an approximate Hamilton decomposition. More precisely, we show that in this range Gn,p contains a set of edge-disjoint Hamilton cyclesâ€¦ (More)

We show that provided log n/n â‰¤ p â‰¤ 1 âˆ’ nâˆ’1/4 log n we can with high probability find a collection of bÎ´(G)/2c edge-disjoint Hamilton cycles in G âˆ¼ Gn,p, plus an additional edge-disjoint matching ofâ€¦ (More)

BÃ¶ttcher, Schacht and Taraz [6] gave a condition on the minimum degree of a graph G on n vertices that ensures G contains every r-chromatic graph H on n vertices of bounded degree and of bandwidthâ€¦ (More)

Given Î· âˆˆ [0, 1], a colouring C of V (G) is an Î·-majority colouring if at most Î·d+(v) out-neighbours of v have colour C(v), for any v âˆˆ V (G). We show that every digraph G equipped with an assignmentâ€¦ (More)

In this thesis we prove three main results on embeddings of spanning subgraphs into graphs and hypergraphs. The first is that for log n/n 6 p 6 1âˆ’nâˆ’1/4 log n, a binomial random graph G âˆ¼ Gn,pâ€¦ (More)