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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Bend-Bounded Path Intersection Graphs: Sausages, Noodles, and Waffles on a Grill
verfasst von : Steven Chaplick, Vít Jelínek, Jan Kratochvíl, Tomáš Vyskočil
Erschienen in: Graph-Theoretic Concepts in Computer Science
Verlag: Springer Berlin Heidelberg
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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.