画线轴花边图或周期图子类的基本圈
Drawing bobbin lace graphs, or, Fundamental cycles for a subclass of periodic graphs
摘要：
在本文中，我们研究了一类由线轴花边图案产生的图形绘制。图纸是周期性的，需要一个组合嵌入与特定的属性，我们概述和证明可以在线性时间验证。此外，花边图的绘制有一个拓扑要求：它包含一组不可收缩的有向环，这些有向环必须与$(1,0)$同伦，也就是说，当绘制在环面上时，每个环围绕次子午线轴缠绕一次，围绕长经度轴缠绕零次。我们提供了一个算法，找到两个基本的循环的一个典型的矩形模式在超图，强制执行这个拓扑约束。然后使用多边形模式在矩形框架内生成花边图的直线图。我们认为，这样的多边形模式总是存在的组合嵌入满足条件的线轴花边模式，因此，我们可以创建一个模式，给定一个图形与固定的组合嵌入的属1。
英文摘要：
In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to $(1,0)$, that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
