A polynomial-time algorithm for the maximum cardinality cut problem in proper interval graphs

It is known that the maximum cardinality cut problem is NP-hard even in chordal graphs. On the positive side, the problem is known to be polynomial time solvable in some subclasses of proper interval graphs which is in turn a subclass of chordal graphs. In this paper, we consider the time complexity of the problem in proper interval graphs, and propose a polynomial-time dynamic programming algorithm.