Therese Biedl ; Michal Stern - On edge-intersection graphs of k-bend paths in grids

dmtcs:482 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 1 - https://doi.org/10.46298/dmtcs.482
On edge-intersection graphs of k-bend paths in grids

Authors: Therese Biedl ; Michal Stern

    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.


    Volume: Vol. 12 no. 1
    Published on: January 1, 2010
    Imported on: March 26, 2015
    Keywords: Intersection graphs,planar graphs,graph drawing,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Funder: Natural Sciences and Engineering Research Council of Canada

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