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arXiv · 1206.5159

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

Steven Chaplick·Vít Jelínek·Jan Kratochvíl·Tomáš Vyskočil
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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.

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Steven Chaplick, Vít Jelínek, Jan Kratochvíl, Tomáš Vyskočil. 2012-06-22. Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill. https://arxiv.org/abs/1206.5159

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