This article is cited in 12 papers

Acyclic 4-coloring of plane graphs without cycles of length 4 and 6

O. V. Borodin

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: Every planar graph is known to be acyclically 5-colorable (Borodin, 1976), which bound is precise. Some sufficient conditions are also obtained for a planar graph to be acyclically 4-colorable. In particular, the acyclic 4-colorability was proved for the following planar graphs: without 3- and 4-cycles (Borodin, Kostochka and Woodall, 1999), without 4-, 5- and 6-cycles, (Montassier, Raspaud and Wang, 2006), without 4-, 6- and 7-cycles, and without 4-, 6- and 8-cycles (Chen, Raspaud, and Wang, 2009).
In this paper it is proved that each planar graph without 4- and 6-cycles is acyclically 4-colorable. Bibl. 17.

Keywords: planar graph, acyclically coloring, acyclic choosability.

UDC: 519.172

Received: 13.05.2009
Revised: 17.06.2009

 English version: Journal of Applied and Industrial Mathematics, 2010, 4:4, 490–495

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