For a directed graph G without loops or parallel edges, let (G) denote the size of the smallest feedback arc set, i.e., the smallest subset X E(G) such that G \ X has no directed...
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
Abstract: In any r-uniform hypergraph H for 2 t r we define an runiform t-tight Berge-cycle of length , denoted by C(r,t) , as a sequence of distinct vertices v1, v2, . . . , v ,...
The problem of the existence of an alternating simple dicycle in a 2-arc-coloured digraph is considered. This is a generalization of the alternating cycle problem in 2-edgecoloure...