Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-99-06

June 1999

Colouring the Square of a Planar Graph

Jan van den Heuvel and Sean McGuinness

Abstract

We prove that for any planar graph G with maximum degree \Delta it holds that the chromatic number of the square of G satisfies \chi(G²) <= 2 \Delta + 25. We generalise this result to integer labellings of planar graphs involving constraints on distances one and two in the graph.

Keywords: planar graph, chromatic number, labelling of a graph.

AMS Subject Classifications (1991)}: 05C10, 05C15.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-171-955 7732. Fax: +44(0)-171-955 6877. Email: info@maths.lse.ac.uk