Carleton University
Technical Report TR-03-03
May 2003
Grid Drawings of k-Colourable Graphs
David Wood
Abstract
It is proved that every k -colourable graph on n vertices has a grid drawing with O ( kn ) area, and that this bound is best possible. This result can be viewed as a generalisation of the no-three-in-line problem. A further area bound is established that includes the aspect ratio as a parameter.