On some special classes of contact $B_0$-VPG graphs

Discrete Applied Mathematics 308 (2022), 111-129 A graph $G$ is a $B_0$-VPG graph if one can associate a path on a rectangular grid with each vertex such that two vertices are adjacent if and only if the corresponding paths intersect at at least one grid-point. A graph $G$ is a contact $B_0$-VPG gra...

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Bibliographic Details
Main Authors Bonomo-Braberman, Flavia, Mazzoleni, María Pía, Rean, Mariano Leonardo, Ries, Bernard
Format Journal Article
LanguageEnglish
Published 19.07.2018
Subjects
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Summary:Discrete Applied Mathematics 308 (2022), 111-129 A graph $G$ is a $B_0$-VPG graph if one can associate a path on a rectangular grid with each vertex such that two vertices are adjacent if and only if the corresponding paths intersect at at least one grid-point. A graph $G$ is a contact $B_0$-VPG graph if it is a $B_0$-VPG graph admitting a representation with no two paths crossing and no two paths sharing an edge of the grid. In this paper, we present a minimal forbidden induced subgraph characterisation of contact $B_0$-VPG graphs within four special graph classes: chordal graphs, tree-cographs, $P_4$-tidy graphs and $P_5$-free graphs. Moreover, we present a polynomial-time algorithm for recognising chordal contact $B_0$-VPG graphs.
DOI:10.48550/arxiv.1807.07372