## Discrete Math Seminar: Steve Chaplick

- Date: 05/22/2012
- Time: 14:30

Simon Fraser University

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 forevery fixed k,

B_k-VPG is a strict subset of B_{k+1}-VPG and that recognition of graphs

from B_k-VPG is NP-complete even when the input graph is givenby 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.

This is joint work with Vit Jelinek, Jan Kratochvil, and Tomas Vyskocil.

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