On some special classes of contact B_0-VPG graphs
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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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