In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondance with their vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. We examine this class ] from a structural point of view which leads to constant upper bounds on the clique number , the chromatic number and the clique chromatic number. We further investigate the relation between planar graphs and CPG graphs and show that CPG graphs are not necessarily planar and not all planar graphs are CPG . Our class generalizes the well studied class of VCPG graphs .
In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. Our class generalizes the well studied class of VCPG graphs (see 1]). We examine CPG graphs from a structural point of view which leads to constant upper bounds on the clique number and the chromatic number. Moreover, we investigate the recognition and 3-colorability problems for B_0-CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG .
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correspondance
correspondence
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We examine this class
Our class generalizes the well studied class of VCPG graphs (see
A
1
A
). We examine CPG graphs
R
, the chromatic number and the clique
and the
R
We further investigate the relation between planar graphs and CPG graphs and
Moreover, we investigate the recognition and 3-colorability problems for B_0-CPG, a subclass of CPG. We further
D
. Our class generalizes the well studied class of VCPG graphs