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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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The Grundy number of the plane
by
Matthew Walsh
Indiana-Purdue University Fort Wayne
Coauthors: Christopher Maier, University of Texas-Dallas

Determining the chromatic number of the unit distance graph in the plane is a celebrated problem in colouring theory; the best currently results place it between 4 and 7. The Grundy number of a (finite) graph is the maximum number of colours that could be used in a greedy colouring of the graph's vertices. We extend the definition of the Grundy number of apply to infinite graphs, and show that the Grundy number of the plane is much, much larger than its chromatic number.

Date received: April 24, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-38.