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


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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