We establish a new lower bound on the l-wise collective minimum degree which guarantees the existence of a perfect matching in a k-uniform hypergraph, where 1 ≤ l < k/2. For l = 1, this improves a… (More)

Riis [Electron. J. Combin., 14(1):R44, 2007] introduced a guessing game for graphs which is equivalent to finding protocols for network coding. In this paper we prove upper and lower bounds for the… (More)

For integers n ≥ k > l ≥ 1 and k-graphs F , define tl (n, F ) to be the smallest integer d such that every k-graph H of order n with minimum l-degree δl(H) ≥ d contains an F -factor. A classical… (More)

The Alon-Roichman theorem states that for every ε > 0 there is a constant c(ε), such that the Cayley graph of a finite group G with respect to c(ε) log |G| elements of G, chosen independently and… (More)

In this paper we discuss the two variable Ising polynomials in a graph theoretical setting. This polynomial has its origin in physics as the partition function of the Ising model with an external… (More)

We describe several computational validations of the asymptotic matching conjectures for r-regular bipartite graphs. These validations are based on algorithms for computation of d-dimensional… (More)

Define a graph to be a Kotzig graph if it is m-regular and has an m-edge colouring in which each pair of colours form a Hamiltonian cycle. We show that every cubic graph with spanning subgraph… (More)

For many of the unsolved problems concerning cycles and matchings in graphs it is known that it is su cient to prove them for snarks, the class of nontrivial 3-regular graphs which cannot be 3-edge… (More)