English

On the Maximum Cardinality Cut Problem in Proper Interval Graphs and Related Graph Classes

Data Structures and Algorithms 2020-06-09 v1 Computational Complexity

Abstract

Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the maximum cardinality cut problem in classes of graphs containing proper interval graphs and mixed unit interval graphs when parameterized by some new parameters that we introduce. These new parameters are related to a generalization of the so-called bubble representations of proper interval graphs and mixed unit interval graphs and to clique-width decompositions.

Keywords

Cite

@article{arxiv.2006.03856,
  title  = {On the Maximum Cardinality Cut Problem in Proper Interval Graphs and Related Graph Classes},
  author = {Arman Boyacı and Tınaz Ekim and Mordechai Shalom},
  journal= {arXiv preprint arXiv:2006.03856},
  year   = {2020}
}
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