无链可嵌入图的补问题
The Complement Problem for Linklessly Embeddable Graphs
摘要：
我们发现所有的最大无链接嵌入图的顺序为11，并验证，对于每一个图$G$的顺序为11，无论是$G$或其补充$cG$是内在联系的。我们给出了一个11阶图$G$的例子，使得$G$和$cG$都是$K_6$ -小自由的。我们提供了最小阶的例子，最大无链嵌入图，不是三角形或3-连接。证明了顶点数不超过11的图的Colin de Verdière不变量的Nordhaus-Gaddum型猜想。我们给出了搜索中使用的程序的描述。
英文摘要：
We find all maximal linklessly embeddable graphs of order up to 11, and verify that for every graph $G$ of order 11 either $G$ or its complement $cG$ is intrinsically linked. We give an example of a graph $G$ of order 11 such that both $G$ and $cG$ are $K_6$-minor free. We provide minimal order examples of maximal linklessly embeddable graphs that are not triangular or not 3-connected. We prove a Nordhaus-Gaddum type conjecture on the Colin de Verdière invariant for graphs on at most 11 vertices. We give a description of the programs used in the search.
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