Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill
Computational Geometry
2012-06-25 v1 Discrete Mathematics
Combinatorics
Abstract
In this paper we study properties of intersection graphs of k-bend paths in the rectangular grid. A k-bend path is a path with at most k 90 degree turns. The class of graphs representable by intersections of k-bend paths is denoted by B_k-VPG. We show here that for every fixed k, B_k-VPG is a proper subset of B_{k+1}-VPG and that recognition of graphs from B_k-VPG is NP-complete even when the input graph is given by a B_{k+1}-VPG representation. We also show that the class B_k-VPG (for k>0) is in no inclusion relation with the class of intersection graphs of straight line segments in the plane.
Keywords
Cite
@article{arxiv.1206.5159,
title = {Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill},
author = {Steven Chaplick and Vít Jelínek and Jan Kratochvíl and Tomáš Vyskočil},
journal= {arXiv preprint arXiv:1206.5159},
year = {2012}
}
Comments
17 pages, 14 figures, to appear in the proceedings of WG 2012