投影面上最优 1 嵌入图的 Re-1 嵌入

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-10-24 DOI:10.1016/j.dam.2024.10.005

Yusuke Suzuki

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引用次数: 0

摘要

Schumacher (1986) 和 Suzuki (2010) 的研究表明，球面上的每个最优 1 嵌入图最多有 8 个不等价 1 嵌入。在本文中，我们证明了投影平面上的最优 1- 嵌入图的不等价 1- 嵌入的数量最多为 24，而该图的四角子图是双方形的。在这种四角形子图是非双方形的情况下，我们证明了一个最优 1 嵌入图在任意大整数 p 下至少有 p 个不等价 1 嵌入。

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Re-1-embeddings of optimal 1-embedded graphs on the projective plane

It was shown in Schumacher (1986), Suzuki (2010) that every optimal 1-embedded graph on the sphere has at most 8 inequivalent 1-embeddings. In this paper, we prove that the number of inequivalent 1-embeddings of an optimal 1-embedded graph on the projective plane whose quadrangular subgraph is bipartite is at most 24. In the case where such quadrangular subgraphs are nonbipartite, we show an optimal 1-embedded graph having at least

p

inequivalent 1-embeddings for any large integer

p

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.