Characterising circular-arc contact $B_0$-VPG graphs

TL;DR

This paper characterizes contact $B_0$-VPG graphs within circular-arc graphs, identifying minimal forbidden induced subgraphs and providing a polynomial-time recognition algorithm.

Contribution

It offers a minimal forbidden induced subgraph characterization and a polynomial-time recognition algorithm for contact $B_0$-VPG graphs within circular-arc graphs.

Findings

Minimal forbidden induced subgraph characterization established.

Polynomial-time recognition algorithm developed.

Recognition is NP-complete in general, but tractable within this class.

Abstract

A contact $B_0$-VPG graph is a graph for which there exists a collection of nontrivial pairwise interiorly disjoint horizontal and vertical segments in one-to-one correspondence with its vertex set such that two vertices are adjacent if and only if the corresponding segments touch. It was shown by Deniz et al. that Recognition is $\mathsf{NP}$-complete for contact $B_0$-VPG graphs. In this paper we present a minimal forbidden induced subgraph characterisation of contact $B_0$-VPG graphs within the class of circular-arc graphs and provide a polynomial-time algorithm for recognising these graphs.