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Erschienen in:
01.11.2015
List 2-distance coloring of planar graphs
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 4/2015
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Abstract
The \(2\)-distance coloring of a graph \(G\) is to color the vertices of \(G\) so that every two vertices at distance at most \(2\) from each other get different colors. Let \(\chi _{2}^{l}(G)\) be the list 2-distance chromatic number of \(G\). In this paper, we show that (1) a planar graph \(G\) with \(\Delta (G)\ge 12\) which contains no \(3,5\)-cycles and intersecting 4-cycles has \(\chi _{2}^{l}(G)\le \Delta +6\); (2) a planar graph \(G\) with \(\Delta (G)\le 5\) and \(g(G)\ge 5\) has \(\chi _{2}^{l}(G)\le 13\).