Discussiones Mathematicae Graph Theory 31(4) (2011) 775-789
doi: 10.7151/dmgt.1579

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Planar graphs without 4-, 5- and 8-cycles are 3-colorable

Sakib A. Mondal

Enterprise Analytics Group
India Science Lab, General Motors Global Research and Development
GM Technical Centre India Pvt Ltd, Creator Bldg., International Tech Park Ltd.
Whitefield Road, Bangalore 560 066, INDIA


In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.

Keywords: 3-coloring, planar graph, discharging

2010 Mathematics Subject Classification: 05C15.


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Received 5 April 2010
Accepted 26 November 2010