Characterising circular-arc contact B_0-VPG graphs
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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 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.
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