$$K_4$$ 小自由图的注入色度指数

Pub Date : 2024-06-04 DOI:10.1007/s00373-024-02807-3

Jian-Bo Lv, Jiacong Fu, Jianxi Li

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引用次数: 0

摘要

如果对于任意两条不同的边$e_1$和$e_2$来说，如果它们在 G 中的距离是 2 或者在一个共同的三角形中，那么它们的颜色就是不同的，那么图 G 的边着色就是可注入的。G 的注入色度指数（(\chi ^\prime _{inj}(G)\)）是 G 的注入边着色所需的最少颜色数。在本说明中，我们证明了每个具有最大度的$\Delta (G)\ge 3$ 的$K_4$-minor free graph G 都满足$\chi ^\prime _{inj}(G)\le 2\Delta (G)+1$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Injective Chromatic Index of $$K_4$$ -Minor Free Graphs

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Injective Chromatic Index of $$K_4$$ -Minor Free Graphs

An edge-coloring of a graph G is injective if for any two distinct edges $e_1$ and $e_2$, the colors of $e_1$ and $e_2$ are distinct if they are at distance 2 in G or in a common triangle. The injective chromatic index of G, $\chi ^\prime _{inj}(G)$, is the minimum number of colors needed for an injective edge-coloring of G. In this note, we show that every $K_4$-minor free graph G with maximum degree $\Delta (G)\ge 3$ satisfies $\chi ^\prime _{inj}(G)\le 2\Delta (G)+1$.

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