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

Steven Chaplick, Vít Jelínek, Jan Kratochvíl, Tomás Vyskocil

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


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 \(\subsetneq\) 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.
Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science. WG 2012
EditorsM.C. Golumbic, M. Stern, A. Levy, G. Morgenstern
PublisherSpringer, Berlin, Heidelberg
Publication statusPublished - 2012
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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