In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prov...
Abstract. For a nite multigraphG, the reliability function of G is the probability RG(q) that if each edge of G is deleted independently with probability q then the remaining edges...
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to...
An acyclic edge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest...
Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in schedu...
Frederic Dorn, Hannes Moser, Rolf Niedermeier, Mat...