$$K_4$$ 小自由图的注入色度指数

IF 0.6 4区数学 Q3 MATHEMATICS

Graphs and Combinatorics 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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来源期刊

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.