框架4-叶图：欧拉回路、高斯回路和旋转回路
Framed 4-Valent Graphs: Euler Tours, Gauss Circuits and Rotating Circuits
摘要：
本文给出了一个显式公式，只要高斯回路存在，就可以从图上的任意欧拉回路直接描述框架4-价图（具有对边结构的图）上的唯一高斯回路。该公式仅依赖于Euler环的邻接矩阵，同时也能给出框架4-度图上是否存在Gauss环。事实证明，这些结果对所有的对称矩阵都是有效的（不仅仅是用弦图可以实现的）。
英文摘要：
In the present paper we give an explicit formula which allows us immediately to describe a unique Gauss circuit on a framed 4-valent graph (a graph with a structure of opposite edges) from an arbitrary Euler tour on the graph whenever the Gauss circuit exists. This formula only depends on the adjacency matrix of an Euler tour and also tells us whether there exists a Gauss tour on a framed 4-valent graph or not. It turns out that the results are also valid for all symmetric matrices (not just realisable by a chord diagram).
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。
