Characterization and a 2D Visualization of B$_0$-VPG Cocomparability Graphs

TL;DR

This paper characterizes B$_0$-VPG cocomparability graphs, providing a polynomial recognition algorithm and a visualization method that reveals the poset structure of the graph.

Contribution

It offers the first characterization of B$_0$-VPG cocomparability graphs and introduces a polynomial-time recognition and visualization algorithm.

Findings

Characterization of B$_0$-VPG cocomparability graphs

Polynomial-time recognition algorithm

Visualization method revealing poset structure

Abstract

B$_0$-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B$_0$-VPG permutation graphs. We respond here by characterizing B$_0$-VPG cocomparability graphs. This characterization also leads to a polynomial time recognition and B$_0$-VPG drawing algorithm for the class. Our B$_0$-VPG drawing algorithm starts by fixing any one of the many posets $P$ whose cocomparability graph is the input graph $G$. The drawing we obtain not only visualizes $G$ in that one can distinguish comparable pairs from incomparable ones, but one can also identify which among a comparable pair is larger in $P$ from this visualization.