A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
Suppose that D is an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let d(D) denote the number of dependent arcs in D. Defi...
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
Abstract. Many graph drawing algorithms use st-numberings (st-orientations or bipolar orientations) as a first step. An st-numbering of a biconnected undirected graph defines a d...
: In this paper we deal with the arc ranking problem of directed graphs. We give some classes of graphs for which the arc ranking problem is polynomially solvable. We prove that de...