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<p>A vertex coloring of a graph <i>G</i> is called a 2-distance coloring if any two vertices at distance at most 2 from each other receive different colors. Let <i>G</i> be a planar graph with girth at least five and maximum degree Δ. We prove that <i>G</i> admits a 2-distance coloring with Δ + 4 colors when Δ ≥ 22, which improves a result of Dong and Lin (Discrete Appl. Math. 217: 495–505, 2017).</p>

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On 2-distance (Δ + 4)-coloring of Planar Graphs with girth Five

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Zakir Deniz

摘要

A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at distance at most 2 from each other receive different colors. Let G be a planar graph with girth at least five and maximum degree Δ. We prove that G admits a 2-distance coloring with Δ + 4 colors when Δ ≥ 22, which improves a result of Dong and Lin (Discrete Appl. Math. 217: 495–505, 2017).