A polynomial time algorithm for strong edge coloring of partial k-trees

A matching M in a graph is called induced if there is no edge in the graph connecting two edges of M. The strong edge coloring problem is to find an edge coloring of a given graph with minimum number of colors such that each color class is an induced matching. This problem is known to be NP-complete, even in very restricted cases. Here, we show that it can be solved in polynomial time on graphs with bounded treewidth, i.e partial k-trees. This answers an open question of Mahdian (Discrete Appl. Math. 118 (2002) 239).