规则和半规则网格中的自避免闭合曲线

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-08-14 DOI:10.1016/j.dam.2025.08.023

Lidija Čomić , Paola Magillo

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引用次数: 0

摘要

我们考虑平面上三个规则网格和八个半规则网格中的封闭曲线，其中每个顶点和每个边可以重复有限次。我们定义了这种曲线的自回避条件，并给出了一种线性时间算法来检验它们。我们定义这些曲线的方向。我们提出了它们的顶点的分类，我们给出了一个统一的公式有关不同类型的顶点的数量，有效的规则和半规则网格。我们的结果可用于平面平铺应用。

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Self-avoiding closed curves in the regular and semiregular grids

We consider closed curves in the three regular and eight semiregular grids in the plane, in which each vertex and each edge can be repeated a limited number of times. We define the conditions for such curves to be self-avoiding, and we present a linear-time algorithm to check them. We define the orientation of such curves. We propose a classification of their vertices, and we give a unifying formula relating the number of different types of vertices, valid in the regular and semiregular grids. Our results can be used in the plane tiling applications.

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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.