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 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∈≥∈1) is in no inclusion relation with the class of intersection graphs of straight line segments in the plane. © 2012 Springer-Verlag Berlin Heidelberg.