TY - GEN
T1 - Edge-intersection graphs of k-bend paths in grids
AU - Biedl, Therese
AU - Stern, Michal
PY - 2009/12/1
Y1 - 2009/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=76249120368&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02882-3_10
DO - 10.1007/978-3-642-02882-3_10
M3 - Conference contribution
AN - SCOPUS:76249120368
SN - 3642028810
SN - 9783642028816
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 86
EP - 95
BT - Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
T2 - 15th Annual International Conference on Computing and Combinatorics, COCOON 2009
Y2 - 13 July 2009 through 15 July 2009
ER -