论文标题
两分的固有打结的图形和23个边缘
Bipartite intrinsically knotted graphs with 23 edges
论文作者
论文摘要
如果每个嵌入都包含一个非试图打结的循环，则将图形在本质上打结。众所周知，本质上打结的图具有至少21个边缘，并且恰好有14个本质上打结的图形，带有21个边缘，其中Heawood图是唯一的两部分图。作者表明，恰好有两个图的最小边缘是较小的两分，本质上打结了：Heawood Graph和Cousin 110 $ e_9+e $ tamess。在本文中，我们表明，恰好有六个两分的本质上打结的图形，有23个边缘，因此每个顶点具有3度或以上。其中有四个包含Heawood图，另外两个包含$ E_9+E $家族的堂兄110。因此，没有少量的最小固有打结的图，其边缘是两部分。
A graph is intrinsically knotted if every embedding contains a nontrivially knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that there are exactly 14 intrinsically knotted graphs with 21 edges, in which the Heawood graph is the only bipartite graph. The authors showed that there are exactly two graphs with at most 22 edges that are minor minimal bipartite intrinsically knotted: the Heawood graph and Cousin 110 of the $E_9+e$ family. In this paper we show that there are exactly six bipartite intrinsically knotted graphs with 23 edges so that every vertex has degree 3 or more. Four among them contain the Heawood graph and the other two contain Cousin 110 of the $E_9+e$ family. Consequently, there is no minor minimal intrinsically knotted graph with 23 edges that is bipartite.
