A linear time algorithm for edge coloring of binomial trees Original Research Article

We consider the problem of efficient coloring of the edges of a so-called binomial tree T, i.e. acyclic graph containing two kinds of edges: those which must have a single color and those which are to be colored with L consecutive colors, where L is an arbitrary integer greater than 1. We give an O(n) time algorithm for optimal coloring of such a tree, where n is the number of vertices of T. Also, we give simple bounds on the chromatic index of T and a division of all binomial trees into two classes depending on their chromaticity.