On some special classes of contact B₀-VPG graphs

Abstract

A graph G is a B₀-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 contact B₀-VPG graph if it is a B₀-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 B₀-VPG graphs within four special graph classes: chordal graphs, tree-cographs, P₄-tidy graphs and P5-free graphs. Moreover, we present a polynomial-time algorithm for recognising chordal contact B₀-VPG graphs.