Discussiones Mathematicae Graph Theory 32(1) (2012)
141-151
DOI: https://doi.org/10.7151/dmgt.1592
2-distance 4-colorability of Planar Subcubic Graphs with Girth at least 22
Oleg V. Borodin Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, and Novosibirsk State University, Novosibirsk, 630090, Russia | Anna O. Ivanova
Institute of Mathematics at Yakutsk State University and |
Abstract
The trivial lower bound for the 2-distance chromatic number χ2(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ2 = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ2(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
Keywords: planar graph, subcubic graph, 2-distance coloring
2010 Mathematics Subject Classification: 05C15.
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Received 23 November 2010
Revised 24 March 2011
Accepted 26 March 2011
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