Characterising circular-arc contact B0–VPG graphs

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-toone correspondence with its vertex set such that two vertices are adjacent if and only if the corresponding segments touch. It was shown in [15] that Recognition is 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.