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arXiv · 1807.07372

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

Flavia Bonomo-Braberman·María Pía Mazzoleni·Mariano Leonardo Rean·Bernard Ries
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Abstract

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.

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Flavia Bonomo-Braberman, María Pía Mazzoleni, Mariano Leonardo Rean, Bernard Ries. 2019-10-03. On some special classes of contact $B_0$-VPG graphs. https://doi.org/10.1016/j.dam.2019.10.008

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