高斯图的圆图（弦交错图）：可实现高斯图的描述，算法，enumeration
Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration
摘要：
弦图，在高斯图的名称下，在低维拓扑中用作研究曲线或结的重要工具。那些对应于曲线或节点的高斯图被称为可实现的。本文的主题是高斯图的可实现性可以通过它的圆图来表示。因此，可以定义和研究可实现的圆图（其中圆图的可实现性被理解为与该图相对应的弦图中的任何一个的可实现性）。一些研究包含了旨在证明这一事实的定理。我们检查这些描述的实验和发现反例的描述可实现的高斯图在这些出版物中的一些。我们制定了新的可实现的圆图的描述，并提出了一个优雅的算法来检查圆图是否是可实现的。我们列举可实现的圆图的小尺寸和评论这些数字。然后，我们集中在一种类型的曲线，称为曲折，并研究其高斯图的圆图。
英文摘要：
Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to curves or knots are called realizable. The theme of our paper is the fact that realizability of a Gauss diagram can be expressed via its circle graph. Accordingly, one can define and study realizable circle graphs (with realizability of a circle graph understood as realizability of any one of chord diagrams corresponding to the graph). Several studies contain theorems purporting to prove the fact. We check several of these descriptions experimentally and find counterexamples to the descriptions of realizable Gauss diagrams in some of these publications. We formulate new descriptions of realizable circle graphs and present an elegant algorithm for checking if a circle graph is realizable. We enumerate realizable circle graphs for small sizes and comment on these numbers. Then we concentrate on one type of curves, called meanders, and study the circle graphs of their Gauss diagrams.
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