Abstract
A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list (\(\varDelta +3\))-coloring for graphs with maximum average degree less than \(\frac{8}{3}\) and maximum degree \(\varDelta \ge 4\) as well as graphs with maximum average degree less than \(\frac{14}{5}\) and maximum degree \(\varDelta \ge 6\).
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Funding
This work was partially supported by the grant HOSIGRA funded by the French National Research Agency (ANR, Agence Nationale de la Recherche) under the contract number ANR-17-CE40-0022.
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This work was partially supported by the grant HOSIGRA funded by the French National Research Agency (ANR, Agence Nationale de la Recherche) under the contract number ANR-17-CE40-0022.
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La, H. 2-Distance List \((\varDelta +3)\)-Coloring of Sparse Graphs. Graphs and Combinatorics 38, 167 (2022). https://doi.org/10.1007/s00373-022-02572-1
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DOI: https://doi.org/10.1007/s00373-022-02572-1