Acyclic colorings of planar graphs
Discrete Mathematics
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Splitting a graph into disjoint induced paths or cycles
Discrete Applied Mathematics
Minimum-width grid drawings of plane graphs
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
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, q=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 Pen@?aloza 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 Pen@?aloza and F.J. Zaragoza Martinez.