Abstract In this note we show every orientation of a connected cubic graph admits an oriented 8-colouring. This lowers the best-known upper bound for the chromatic number of the family of orientations of connected cubic graphs. We further show that every such oriented graph admits a 2-dipath 7-colouring. These results imply that either the oriented chromatic number for the family of orientations of connected cubic graphs equals the 2-dipath chromatic number or the long-standing conjecture of Sopena (Sopena, 1997) regarding the chromatic number of orientations of connected cubic graphs is false.

中文翻译：

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有向连通三次图的着色

摘要 在这篇笔记中，我们展示了连通三次图的每个方向都允许有方向的 8 色。这降低了连通三次图的方向族的色数的最著名的上限。我们进一步表明，每个这样的定向图都承认 2-dipath 7-coloring。这些结果意味着连接立方图的方向族的有向色数等于 2-dipath 色数或 Sopena (Sopena, 1997) 关于连通立方图的方向色数的长期猜想是错误的.