Regular and canonical colorings

Abstract

A general framework for coloring problems is described; the concept of regular coloring is introduced; it simply means that one specifies in each edge the maximum and the minimum number of nodes which may have the same color. For several types of regular colorings, one defines canonical colorings where colors form an ordered set and where one always tries to use first the “smallest” colors. It is shown that for some classes of multigraphs including bipartite multigraphs, regular edge colorings corresponding to maximal color feasible sequences are canonical.