A graph G is a B0-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 B0-VPG graph if it is a B0-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 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.Comment: 34 pages, 15 figure