Bend-bounded path intersection graphs: sausages, noodles, and waffles on a grill

Authors:
Steven Chaplick;Vít Jelínek;Jan Kratochvíl;Tomáš Vyskočil
Affiliations:
Department of Mathematics, Wilfrid Laurier University, Waterloo, CA, Canada;Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

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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 Bk-VPG. We show here that for every fixed k, Bk-VPG $\subsetneq$Bk+1-VPG and that recognition of graphs from Bk-VPG is NP-complete even when the input graph is given by a Bk+1-VPG representation. We also show that the class Bk-VPG (for k≥1) is in no inclusion relation with the class of intersection graphs of straight line segments in the plane.