Acyclic colourings of planar graphs with large girth
OV Borodin, AV Kostochka… - Journal of the London …, 1999 - cambridge.org
OV Borodin, AV Kostochka, DR Woodall
Journal of the London Mathematical Society, 1999•cambridge.orgA 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 χa= 5 and girth g= 4. It is proved here that a planar graph satisfies
χa [les] 4 if g [ges] 5 and χa [les] 3 if g [ges] 7.
that every planar graph is acyclically 5-colourable, and that there are planar graphs with
acyclic chromatic number χa= 5 and girth g= 4. It is proved here that a planar graph satisfies
χa [les] 4 if g [ges] 5 and χa [les] 3 if g [ges] 7.
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 χa = 5 and girth g = 4. It is proved here that a planar graph satisfies χa [les ] 4 if g [ges ] 5 and χa [les ] 3 if g [ges ] 7.
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