Path Coloring

In graph theory, path coloring usually refers to one of two problems:

  • The problem of coloring a (multi)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 (in accordance with the above definition) any chosen (multi)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.

In both the above problems, the goal is usually to minimise the number of colors used in the coloring. In different variants of path coloring, may be a simple graph, digraph or multigraph.

Famous quotes containing the word path:

    “The living language is like a cowpath: it is the creation of the cows themselves, who, having created it, follow it or depart from it according to their whims or their needs. From daily use, the path undergoes change. A cow is under no obligation to stay in the narrow path she helped make, following the contour of the land, but she often profits by staying with it and she would be handicapped if she didn’t know where it was or where it led to.”
    —E.B. (Elwyn Brooks)