Unfolding 3-separated polycube graphs of arbitrary genus

IF 0.4 4区计算机科学 Q4 MATHEMATICS Computational Geometry-Theory and Applications Pub Date : 2023-02-01 DOI:10.1016/j.comgeo.2022.101944

Mirela Damian , Robin Flatland

引用次数: 0

Abstract

A polycube graph is a polyhedron composed of cubes glued together along whole faces, whose surface is a 2-manifold. A polycube graph is 3-separated if no two boxes of degree 3 or higher are adjacent, and no grid edge is entirely surrounded by boxes (i.e., there is no cycle of length 4). We show that every 3-separated polycube graph can be unfolded with a $7 \times 7$ refinement of the grid faces. This result extends the class of well-separated polycube graphs known to have an unfolding by allowing boxes of degree 2 to be adjacent to each other and to higher degree boxes.

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展开任意亏格的3-分离多立方体图

多立方体图是由沿整面粘合在一起的立方体组成的多面体，其表面是一个2流形。如果没有两个度为3或更高的盒子相邻，并且没有网格边缘完全被盒子包围(即，没有长度为4的循环)，则聚立方图是3分离的。我们表明，每个3分离的聚立方图都可以通过7×7网格面的细化展开。这个结果扩展了已知具有展开的分离良好的多立方图的类别，允许2次的框彼此相邻以及更高次的框。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.

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