Bipartite permutation graphs

Bipartite graphs and permutation graphs are two well known subfamilies of the perfect graphs. Neither of these families is contained in the other, and their intersection is nonempty. This paper shows that graphs which are both bipartite and permutation graphs have good algorithmic properties. These graphs can be recognized in linear time, and several problems which are NP-complete or of unknown complexity for graphs in either of the two larger classes can be solved in polynomial time when restricted to bipartite permutation graphs. These problems include the Hamilton Circuit problem, a variant of the Crossing Number problem, and the minimum fill-in problem.