Hoang La ; Mickael Montassier - 2-distance 4-coloring of planar subcubic graphs with girth at least 21

dmtcs:7563 - Discrete Mathematics & Theoretical Computer Science, March 5, 2025, vol. 26:3 - https://doi.org/10.46298/dmtcs.7563
2-distance 4-coloring of planar subcubic graphs with girth at least 21Article

Authors: Hoang La ; Mickael Montassier

    A $2$-distance $k$-coloring of a graph is a proper vertex $k$-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance $4$-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not $2$-distance $4$-colorable.


    Volume: vol. 26:3
    Section: Graph Theory
    Published on: March 5, 2025
    Accepted on: November 1, 2024
    Submitted on: June 9, 2021
    Keywords: Mathematics - Combinatorics,Computer Science - Discrete Mathematics

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