Edge-Intersection Graphs of k-Bend Paths in Grids

Authors:
Therese Biedl;Michal Stern
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Caesarea Rothschild Institute, University of Haifa, Israel, and The Academic College of Tel-Aviv, Yaffo, Israel
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

Edge-intersection graphs of paths in grids are graphs that can be represented with vertices as paths in grids and edges between the vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications in conflict resolution of paths in grid networks. In this paper, we continue the study of edge-intersection graphs of paths in a grid, which was initiated by Golumbic, Lipshteyn and Stern. We show that for any k , if the number of bends in each path is restricted to be at most k , then not all graphs can be represented. Then we study some graph classes that can be represented with k -bend paths, for small k . We show that every planar graph has a representation with 5-bend paths, every outerplanar graph has a representation with 3-bend paths, and every bipartite planar graph has a representation with 2-bend paths.