Edge-Intersection Graphs of k-Bend Paths in Grids
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.
Unable to display preview. Download preview PDF.
- 1.Asinowski, A., Suk, A.: Edge intersection graphs of systems of grid paths with bounded number of bends. Discrete Applied Mathematics (accepted), preliminary version available at, http://www.technion.ac.il/~andrei/epg.pdf
- 6.Golumbic, M.C., Lipshteyn, M., Stern, M.: Edge intersection graphs of single bend paths on a grid. In: Sixth Cologne Twente Workshop on Graphs and Combinatorial Optimization (CTW 2007), University of Twente, pp. 53–55 (2007)Google Scholar