一些完整二方图和三方图的厚度

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI:10.1007/s10255-024-1128-1

Si-wei Hu, Yi-chao Chen

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引用次数: 0

摘要

在本文中，我们得到了 k = 2, 3 时一些完整 k 部分图的厚度。我们首先通过给出 k≥3 时 K4k-1,4k+7 的平面分解来计算 Kn,n+8 的厚度。然后，当 g 为偶数时，得到 K1,g,g(g-1)的两个平面分解；当 g 为奇数时，得到 \(K_{1,g,{1/over{2}}(g-1)^{2}}\) 的两个平面分解。通过递归构造，我们还得到了一些完整三方图的厚度。这里的结果支持了一个存在已久的猜想，即对于任意正整数 m、n，Km,n 的厚度都是\(\lceil {mn\over{2(m+n-2)}}\rceil\) 。

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The Thickness of Some Complete Bipartite and Tripartite Graphs

In this paper, we obtain the thickness for some complete k–partite graphs for k = 2, 3. We first compute the thickness of K_n,n+8 by giving a planar decomposition of K_4k−1,4k+7 for k ≥ 3. Then, two planar decompositions for K_1,g,g(g−1) when g is even and for \(K_{1,g,{1\over{2}}(g-1)^{2}}\) when g is odd are obtained. Using a recursive construction, we also obtain the thickness for some complete tripartite graphs. The results here support the long-standing conjecture that the thickness of K_m,n is \(\lceil {mn\over{2(m+n-2)}}\rceil\) for any positive integers m, n.

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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.