Linear embeddings of $K_9$ are triple linked

Abstract

We use the theory of oriented matroids to show that any linear embedding of $K_9$, the complete graph on nine vertices, contains a non-split link with three components.

7 pages, 1 figure. An updated Mathematica program and five files containing evidence that the program works correctly are available as ancillary files associated with this article

Cited by in corpus (2)

• On the number of links in a linearly embedded $K_{3,3,1}$
• Weakly linked embeddings of pairs of complete graphs in ${\mathbb{R}}^3$