Grid drawings of k-colourable graphs

Authors:
David R. Wood
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2005

Citing 2
Cited 3

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h-quasi planar drawings of bounded treewidth graphs in linear area

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science

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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.