@article{f6360194fe9948debd67de505b506966,
title = "Acyclic colourings of planar graphs with large girth",
abstract = "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 ≤ 4 if g ≥ 5 and χa ≤ 3 if g ≥ 7.",
author = "Borodin, {O. V.} and Kostochka, {A. V.} and Woodall, {D. R.}",
note = "Funding Information: This work was carried out while the first author was visiting Nottingham, funded by Visiting Fellowship Research Grant GR}K00561 from the Engineering and Physical Sciences Research Council. The work of this author was also partly supported by grant NQ4300 of the International Science Foundation and the Russian Government. The work of the second author was partly supported by grant 93-01-01486 of the Russian Foundation of Fundamental Research and grant RPY300 of the International Science Foundation and the Russian Government.",
year = "1999",
month = oct,
doi = "10.1112/S0024610799007942",
language = "English (US)",
volume = "60",
pages = "344--352",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "2",
}