Path coloring

• The problem of coloring a set of paths in graph, in such a way that any two paths of which share an edge in receive different colors. Set and graph are provided at input. This formulation is equivalent to vertex coloring the conflict graph of set, i.e. a graph with vertex set and edges connecting all pairs of paths of which are not edge-disjoint with respect to.
• The problem of coloring any chosen set of paths in, such that the set of pairs of end-vertices of paths from is equal to some set or multiset, called a set of requests. Set and graph are provided at input. This problem is a special case of a more general class of graph routing problems, known as call scheduling.