Abstract
The k-2-distance coloring of graph G is a mapping \(c:V(G)\rightarrow \{1,2,\ldots ,k\}\) such that any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer k such that G has a k-2-distance coloring, denoted by \(\chi _{2}(G)\). In this paper, we prove that every planar graph G without adjacent 5-cycles and \(g(G)\ge 5\) and \(\Delta (G)\ge 17\) has \(\chi _{2}(G)\le \Delta +3\).
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Bu, Y., Zhang, Z. & Zhu, H. 2-Distance coloring of planar graphs without adjacent 5-cycles. J Comb Optim 45, 126 (2023). https://doi.org/10.1007/s10878-023-01053-2
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DOI: https://doi.org/10.1007/s10878-023-01053-2