A vertex coloring of a graph $G$ is said to be a 2-distance coloring if any two vertices at distance at most $2$ from each other receive different colors, and the least number of colors for which $G$ admits a 2-distance coloring is known as the 2-distance chromatic number of $G$, and denoted by $\chi_2(G)$. We prove that if $G$ is a planar graph with girth $5$ and maximum degree $\Delta \geq 12$, then $\chi_2(G)\leq \Delta(G)+5$.
Primary Language | English |
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Subjects | Applied Mathematics (Other) |
Journal Section | Articles |
Authors | |
Early Pub Date | April 28, 2025 |
Publication Date | April 30, 2025 |
Submission Date | November 18, 2024 |
Acceptance Date | April 7, 2025 |
Published in Issue | Year 2025 Volume: 13 Issue: 1 |