A linear algorithm for finding [g, f]-colorings of partial k-trees

In an ordinary edge-coloring of a graph each color appears at each vertex v at most once. A [g, f]-coloring is a generalized edge-coloring in which each color appears at each vertex v at least g(v) and at most f(v) times, where g(v) and f(v) are respectively nonnegative and positive integers assigned to v. This paper gives a linear-time algorithm to find a [g, d]-coloring of a given partial k-tree using the minimum number of colors if there exists a [g, f]-coloring.