On the strong chromatic index and induced matching of tree-cographs,   permutation graphs and chordal bipartite graphs
  We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exist efficient algorithms for the strong chromatic index of (bipartite) permutation graphs and of chordal bipartite graphs. 
Ton Kloks, Chin-Ting Ung and Yue-Li Wang
math.CO