Linear Embeddings of K9 Are Triple Linked
نویسنده
چکیده
We use the theory of oriented matroids to show that any linear embedding of K9, the complete graph on nine vertices, contains a non-split link with three components.
منابع مشابه
Intrinsically Triple Linked Complete Graphs
We prove that every embedding of K10 in R3 contains a non-split link of three components. We also exhibit an embedding of K9 with no such link of three components.
متن کاملON TRIPLE VERONESE EMBEDDINGS OF Pn IN THE GRASSMANNIANS
We classify all the embeddings of Pn in a Grassmannian Gr(1, N) such that the composition with the Plücker embedding is given by a linear system of cubics on Pn. As a direct corollary, we prove that every vector bundle giving such an embedding, splits if n ≥ 3.
متن کاملTriangular embeddings of complete graphs
In this paper we describe the generation of all nonorientable triangular embeddings of the complete graphs K12 and K13. (The 59 nonisomorphic orientable triangular embeddings of K12 were found in 1996 by Altshuler, Bokowski and Schuchert, and K13 has no orientable triangular embeddings.) There are 182, 200 nonisomorphic nonorientable triangular embeddings for K12, and 243, 088, 286 for K13. Tri...
متن کاملTriple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملOn the Ultramean Construction
We use the ultramean construction to prove linear compactness theorem. We also extend the Rudin-Keisler ordering to maximal probability charges and characterize it by embeddings of power ultrameans.
متن کامل