具有独立交叉的外平面图的强边缘着色

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1026-6

Ke-Jie Li, Xin Zhang

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引用次数: 0

摘要

图的强色度指数是指在适当的边着色中，没有一条边与两条相同颜色的边相邻所需的最少颜色数。具有独立交叉的外平面图是这样一种嵌入平面的图：所有顶点都在外侧面上，两对交叉边没有共同的末端顶点。研究证明，如果Δ ≥ 4，则每个具有独立交叉和最大度数Δ的外平面图的强色度指数最多为 4Δ - 6；如果Δ ≤ 3，则强色度指数最多为 8。这两个界限都很尖锐。

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Strong Edge Coloring of Outerplane Graphs with Independent Crossings

The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color. An outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end vertex. It is proved that every outerplane graph with independent crossings and maximum degree Δ has strong chromatic index at most 4Δ − 6 if Δ ≥ 4, and at most 8 if Δ ≤ 3. Both bounds are sharp.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.