Publication at Faculty of Mathematics and Physics |
2013
Abstract
A grid drawing of a graph maps vertices to the grid Z(d) and edges to line segments that avoid grid points representing other vertices. We show that a graph G is q(d)-colorable, d, g >= 2, if and only if there is a grid drawing of G in Z(d) in which no line segment intersects more than q grid points.
This strengthens the result of D. Flores Penaloza 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 Penaloza and F.J. Zaragoza Martinez. (c) 2013 Published by Elsevier B.V.