Skip to Main content Skip to Navigation
Journal articles

On edge-intersection graphs of k-bend paths in grids

Abstract : Edge-intersection graphs of paths in grids are graphs that can be represented such that vertices are paths in a grid and edges between 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 planar bipartite graph has a representation with 2-bend paths. We also study line graphs, graphs of bounded pathwidth, and graphs with -regular edge orientations.
Document type :
Journal articles
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download

https://hal.inria.fr/hal-00990425
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Tuesday, May 13, 2014 - 3:36:14 PM
Last modification on : Wednesday, November 29, 2017 - 10:26:18 AM
Long-term archiving on: : Monday, April 10, 2017 - 10:03:30 PM

File

1322-4851-1-PB.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00990425, version 1

Collections

Citation

Therese Biedl, Michal Stern. On edge-intersection graphs of k-bend paths in grids. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (1), pp.1-12. ⟨hal-00990425⟩

Share

Metrics

Record views

419

Files downloads

1072