4 research outputs found
Characterising circular-arc contact -VPG graphs
A contact -VPG graph is a graph for which there exists a collection of
nontrivial pairwise interiorly disjoint horizontal and vertical segments in
one-to-one correspondence with its vertex set such that two vertices are
adjacent if and only if the corresponding segments touch. It was shown by Deniz
et al. that Recognition is -complete for contact -VPG graphs.
In this paper we present a minimal forbidden induced subgraph characterisation
of contact -VPG graphs within the class of circular-arc graphs and provide
a polynomial-time algorithm for recognising these graphs
Characterising Chordal Contact: Bo-VPG Graphs
A graph G is a Bo- VPG graph if it is the vertex intersection graph of horizontal and vertical paths on a grid. A graph G is a contact Bo- VPG graph if the vertices can be represented by interiorly disjoint horizontal or vertical paths on a grid and two vertices are adjacent if and only if the corresponding paths touch. In this paper, we present a minimal forbidden induced subgraph characterisation of contact Bo-VPG graphs within the class of chordal graphs and provide a polynomial-time algorithm for recognising these graphs