Critical properties of bipartite permutation graphs

TL;DR

This paper investigates the critical subclasses within bipartite permutation graphs, highlighting their significance in understanding graph parameters like clique-width, rank-width, and algorithmic complexity.

Contribution

It identifies and characterizes various critical subclasses of bipartite permutation graphs, advancing the understanding of their structural properties.

Findings

Bipartite permutation graphs contain multiple critical subclasses.

Critical subclasses influence parameters like clique-width and shrub-depth.

The study enhances understanding of hereditary graph classes and their algorithmic implications.

Abstract

The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique- and rank-width of graphs, because it is one of the minimal hereditary classes of graphs of unbounded clique- and rank-width. It also contains a number of important subclasses, which are critical with respect to other parameters, such as graph lettericity or shrub-depth, and with respect to other notions, such as well-quasi-ordering or complexity of algorithmic problems. In the present paper we identify critical subclasses of bipartite permutation graphs of various types.