Lune -自由纽结图
Lune -- Free Knot Graphs
摘要：
本文研究了平面上简单四正则图（即无环图和任意两个结点之间只有一条边）。这些图是三维空间中的结点和链接理论及其平面图的基础。我们将这篇论文献给Frank Harary（1921 - 2005），他对节点图的迷恋激发了这项工作，我们很高兴与他一起开发了这篇论文。我们证明了当v（节点数）大于或等于8时，总存在这样的纽结图.我们的证明产生了一类“紧”的图形，不提交的递归过程，生成图形与v+2节点的“可接受”的图形与v节点。然后，我们对这种紧图进行分类。
英文摘要：
This paper is an exploration of simple four-regular graphs in the plane (i.e. loopless and with no more than one edge between any two nodes). Such graphs are fundamental to the theory of knots and links in three dimensional space, and their planar diagrams. We dedicate this paper to Frank Harary (1921 -- 2005) whose fascination with graphs of knots inspired this work and with whom we had the pleasure of developing this paper. We prove that for v (the number of nodes) greater than or equal to 8 there always exist such knot-graphs. Our proof gives rise to a class of "tight" graphs that do not submit to the recursive procedure that generates graphs with v+2 nodes from "admissible" graphs with v nodes. We then classify such tight graphs.
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。
