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Acyclic Colourings of Planar Graphs with Large Girth

1999; Wiley; Volume: 60; Issue: 2 Linguagem: Inglês

10.1112/s0024610799007942

1469-7750

O. V. Borodin, Alexandr Kostochka, Douglas R. Woodall,

Advanced Graph Theory Research

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.