English

On contact graphs of paths on a grid

Computational Geometry 2018-09-07 v4

Abstract

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 B0B_0-CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG.

Keywords

Cite

@article{arxiv.1803.03468,
  title  = {On contact graphs of paths on a grid},
  author = {Zakir Deniz and Esther Galby and Andrea Munaro and Bernard Ries},
  journal= {arXiv preprint arXiv:1803.03468},
  year   = {2018}
}

Comments

Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)

R2 v1 2026-06-23T00:47:35.040Z