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- W4205307969 abstract "A 2-distance k -coloring of a graph G is a proper k -coloring in which any two vertices with distance at most two get different colors. The 2-distance number is the smallest number k such that G has a 2-distance k -coloring, denote as χ 2 ( G ) . In 1977, Wegner conjectured that for each planar graph G with maximum degree Δ, χ 2 ( G ) ≤ 7 if Δ ≤ 3 , χ 2 ( G ) ≤ Δ + 5 if 4 ≤ Δ ≤ 7 and χ 2 ( G ) ≤ ⌊ 3 Δ 2 ⌋ + 1 if Δ ≥ 8 . In 2001, Thomassen supported the conjecture by proving the case when Δ = 3 . The conjecture is still open even for Δ = 4 . In this paper, we show χ 2 ( G ) ≤ 19 for every planar graph with Δ ≤ 5 which improves a former bound χ 2 ( G ) ≤ 20 ." @default.
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- W4205307969 date "2022-04-01" @default.
- W4205307969 modified "2023-09-30" @default.
- W4205307969 title "2-distance coloring of planar graphs with maximum degree 5" @default.
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- W4205307969 doi "https://doi.org/10.1016/j.disc.2021.112766" @default.
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