Characterising circular-arc contact [formula omitted]–VPG graphs

Abstract

A contactB0–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 in Deniz et al. (2018) that Recognition is NP-complete for contact B0–VPG graphs. In this paper we present a minimal forbidden induced subgraph characterisation of contact B0–VPG graphs within the class of circular-arc graphs and provide a polynomial-time algorithm for recognising these graphs.