Abstract A strong edge-coloring of a graph G = ( V , E ) is a partition of its edge set E into induced matchings. The edge weight of a graph G is defined to be max { d G ( u ) + d G ( v ) | e = u v ∈ E ( G ) } . We study graphs with edge weight at most 7. We show that 1) every graph with edge weight at most 6 has a strong edge-coloring using at most 10 colors; and 2) every graph with edge weight at most 7 has a strong edge-coloring using at most 15 colors.

中文翻译：

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边权重小的图的强边着色

摘要 图 G = ( V , E ) 的强边着色是将其边集 E 划分为诱导匹配。图 G 的边权重定义为 max { d G ( u ) + d G ( v ) | e = uv ∈ E ( G ) } 。我们研究边权重最多为 7 的图。我们表明：1）每个边权重最多为 6 的图都具有使用最多 10 种颜色的强边着色；和 2）每个边权重最多为 7 的图具有最多使用 15 种颜色的强边着色。