In a proper edge-coloring of a cubic graph, an edge $e$ is normal if the set of colors used by the five edges incident with an end of $e$ has cardinality 3 or 5. The Petersen coloring conjecture asserts that every bridgeless cubic graph has a normal 5-edge-coloring, that is, a proper 5-edge-coloring such that all edges are normal. In this paper, we prove a result related to the Petersen coloring conjecture. The parameter ${\mathrm{\mu }}_3$ is a measurement for cubic graphs, introduced by Steffen in 2015. Our result shows that every bridgeless cubic graph $G$ has a proper 5-edge-coloring such that at least $\left|E\left(G\right)\right|-{\mathrm{\mu }}_3\left(G\right)$ (which is no less than $\frac{27}{35}\left|E\left(G\right)\right|$) edges are normal. This result improves on some earlier results of Bílková and Šámal.

在对立方图进行适当的边着色时，边 $Ë$ 如果五个边沿所入射的一组颜色所使用的一组颜色是正常的，则这是正常的 $Ë$具有3或5的基数。Petersen着色猜想断言，每个无桥三次方图都有正常的5边缘着色，即，适当的5边缘着色使得所有边缘都是正常的。在本文中，我们证明了与彼得森着色猜想有关的结果。参数${\mathrm{\mu }}_3$ 是由Steffen在2015年推出的对立方图的度量。我们的结果表明，每个无桥立方图 $G$ 具有适当的5边色，使得至少 $\left|E（G）\right|-{\mathrm{\mu }}_3（G）$ （不少于 $\frac{27}{35}\left|E（G）\right|$）边缘是正常的。此结果比Bílková和Šámal的一些早期结果有所改进。