Thomassen (J. Combin. Theory Ser B 128:192–218, 2018) showed that every subcubic planar graph has 2-distance chromatic number at most 7, which was originally conjectured by Wegner (graphs with given diameter and a coloring problem, University of Dortmund, preprint, 1977). In this note, we consider 3-distance colorings of this family of graphs, and prove that every subcubic planar graph has 3-distance chromatic number at most 17, and we conjecture that this number can be reduced to 12. In addition, we show that every planar graph with maximum degree at most \(\Delta \) has 3-distance chromatic number at most \((6+o(1))\Delta \).

Thomassen (J. Combin. Theory Ser B 128:192–218, 2018) 表明，每个次立方平面图的 2 距离色数最多为 7，这最初是由 Wegner 猜想的（给定直径和着色问题的图，大学多特蒙德，预印本，1977 年）。在这篇笔记中，我们考虑了这组图的 3 距离着色，并证明每个次立方平面图的 3 距离色数最多为 17，并且我们推测这个数可以减少到 12。此外，我们证明每个最大度数最多\(\Delta \)的平面图最多有 3 个距离色数\((6+o(1))\Delta \)。