Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10327396 | Computational Geometry | 2013 | 13 Pages |
Abstract
A grid drawing of a graph maps vertices to the grid Zd and edges to line segments that avoid grid points representing other vertices. We show that a graph G is qd-colorable, d, q⩾2, if and only if there is a grid drawing of G in Zd in which no line segment intersects more than q grid points. This strengthens the result of D. Flores PenÌaloza and F.J. Zaragoza Martinez. Second, we study grid drawings with a bounded number of columns, introducing some new NP-complete problems. Finally, we show that any planar graph has a planar grid drawing where every line segment contains exactly two grid points. This result proves conjectures asked by D. Flores PenÌaloza and F.J. Zaragoza Martinez.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Martin Balko,