On some special classes of contact B_0-VPG graphs

BONOMO, FLAVIA; MAZZOLENI, MARÍA PIA; REAN, MARIANO; RIES, BERNARD

DISCRETE APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2022 vol. 308 p. 111 - 129

0166-218X

A graph $G$ is a $B_0$-VPG graph if one can associate a horizontal or vertical path on a rectangular grid with each vertex such that two vertices are adjacent if and only if the corresponding paths intersect in at least one grid-point. A graph $G$ is a emph{contact $B_0$-VPG graph} if it is a $B_0$-VPG graph admitting a representation with no one-point paths, 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.