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 B0-CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG.
CITATION STYLE
Deniz, Z., Galby, E., Munaro, A., & Ries, B. (2018). On contact graphs of paths on a grid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11282 LNCS, pp. 317–330). Springer Verlag. https://doi.org/10.1007/978-3-030-04414-5_22
Mendeley helps you to discover research relevant for your work.