For a fixed polyomial f Z[X], let k(N) denote the maximum size of a set A {1, 2, . . . , N} such that no product of k distinct elements of A is in the value set of f. In this pap...
Abstract. We show that the tree-width of a graph can be defined without reference to graph vertices, and hence the notion of tree-width can be naturally extended to matroids. (This...
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a p...
We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number L and the antisymmetric flow number Las of an oriented matroid...
We find the asymptotic number of connected graphs with k vertices and k - 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the pro...