Borodin, O. V.; Ivanova, A. O.; Neustroeva, T. K. Sufficient conditions for the 2-distance \((\Delta+1)\)-colorability of planar graphs with girth 6. (Russian) Zbl 1249.05113 Diskretn. Anal. Issled. Oper., Ser. 1 12, No. 3, 32-47 (2005). It is known that (a)\(\Delta+1\) is a lower bound for a 2-distance chromatic number of a graph \(G\) with maximum degree \(\Delta\); (b) if \(G\) is planar and its girth is at least 7 then, for sufficiently large \(\Delta\), this bound is attained; (c) statement (b) is not true for graphs with girth 6. For a planar graph \(G\) with girth 6, \(\Delta\geq 179\), and every edge incident with a vertex of degree 1 or 2, the authors prove that the 2-distance chromatic number of \(G\) is equal to \(\Delta+1\). Reviewer: Victor Alexandrov (Novosibirsk) Cited in 8 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory 05C12 Distance in graphs Keywords:cycle PDFBibTeX XMLCite \textit{O. V. Borodin} et al., Diskretn. Anal. Issled. Oper., Ser. 1 12, No. 3, 32--47 (2005; Zbl 1249.05113)