Let H be any graph. 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). More precisely, let Î´(H,n) denoteâ€¦ (More)

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 threeâ€¦ (More)

A long-standing conjecture of Kelly states that every regular tournament on n vertices can be decomposed into (n âˆ’ 1)/2 edge-disjoint Hamilton cycles. We prove this conjecture for large n. In fact,â€¦ (More)

We show that for each Î· > 0 every digraph G of sufficiently large order n is Hamiltonian if its outand indegree sequences d+1 â‰¤ Â· Â· Â· â‰¤ d + n and dâˆ’1 â‰¤ Â· Â· Â· â‰¤ d âˆ’ n satisfy (i) d + i â‰¥ i + Î·n or d âˆ’â€¦ (More)

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 hypergraphs. Weâ€¦ (More)

We show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr g . This is bestâ€¦ (More)

We show that for each Î± > 0 every sufficiently large oriented graph G with Î´(G), Î´âˆ’(G) â‰¥ 3|G|/8 + Î±|G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen [21]. Inâ€¦ (More)

We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose thatH is a sufficiently large 3-uniform hypergraph whose order n is divisibleâ€¦ (More)