Abstract
A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance (\(\varDelta +1\))-coloring for graphs with maximum average degree less than \(\frac{18}{7}\) and maximum degree \(\varDelta \ge 7\). As a corollary, every planar graph with girth at least 9 and \(\varDelta \ge 7\) admits a 2-distance \((\varDelta +1)\)-coloring. The proof uses the potential method to reduce new configurations compared to classic approaches on 2-distance coloring.
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La, H., Montassier, M. (2021). 2-Distance \((\varDelta +1)\)-Coloring of Sparse Graphs Using the Potential Method. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_54
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DOI: https://doi.org/10.1007/978-3-030-83823-2_54
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