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Acyclic colourings of planar graphs with large girth
 J. London Math. Soc
, 1999
"... A proper vertexcolouring of a graph is acyclic if there are no 2coloured cycles. It is known that every planar graph is acyclically 5colourable, and that there are planar graphs with acyclic chromatic number χ a � 5 and girth g � 4. It is proved here that a planar graph satisfies χ ..."
Abstract

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A proper vertexcolouring of a graph is acyclic if there are no 2coloured cycles. It is known that every planar graph is acyclically 5colourable, and that there are planar graphs with acyclic chromatic number χ a � 5 and girth g � 4. It is proved here that a planar graph satisfies χ