The Maximum Cardinality Cut Problem is Polynomial in Proper Interval Graphs

TL;DR

This paper demonstrates that the maximum cardinality cut problem, known to be NP-hard in chordal graphs, can be solved in polynomial time within proper interval graphs using a dynamic programming approach.

Contribution

The paper introduces a polynomial-time dynamic programming algorithm for the maximum cardinality cut problem specifically in proper interval graphs, a subclass of chordal graphs.

Findings

Maximum cardinality cut problem is polynomial in proper interval graphs.

Proposed dynamic programming algorithm efficiently solves the problem.

Contrasts with NP-hardness in chordal graphs.

Abstract

It is known that the maximum cardinality cut problem is NP-hard even in chordal graphs. In this paper, we consider the time complexity of the problem in proper interval graphs, a subclass of chordal graphs, and propose a dynamic programming algorithm which runs in polynomial-time.