Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill

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.

arXiv comment17 pages, 14 figures, to appear in the proceedings of WG 2012

Cited by in corpus (2)

• On some special classes of contact $B_0$-VPG graphs
• Characterising circular-arc contact $B_0$-VPG graphs