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Journal of the London Mathematical Society 1999 60(2):344-352; doi:10.1112/S0024610799007942
© 1999 by London Mathematical Society
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© The London Mathematical Society

Acyclic Colourings of Planar Graphs with Large Girth

O. V. Borodin, A. V. Kostochka and D. R. Woodall

Institute of Mathematics, Siberian Branch, Russian Academy of Sciences Novosibirsk 630090, Russia
Novosibirsk State University Novosibirsk 630090, Russia
Department of Mathematics, University of Nottingham Nottingham NG7 2RD

Received 20 December 1995. Revision received 26 October 1997.

A proper vertex-colouring of a graph is acyclic if there are no 2-coloured cycles. It is known that every planar graph is acyclically 5-colourable, and that there are planar graphs with acyclic chromatic number {chi}a = 5 and girth g = 4. It is proved here that a planar graph satisfies {chi}a ≤ 4 if g ≥ 5 and {chi}a ≤ 3 if g ≥ 7.


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