Ramsey theorems for knots, links and spatial graphs
Author:
Seiya Negami
Journal:
Trans. Amer. Math. Soc. 324 (1991), 527541
MSC:
Primary 57M25; Secondary 05C10
DOI:
https://doi.org/10.1090/S00029947199110697419
MathSciNet review:
1069741
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Abstract: An embedding $f:G \to {{\mathbf {R}}^3}$ of a graph $G$ into ${{\mathbf {R}}^3}$ is said to be linear if each edge $f(e)\quad (e \in E(G))$ is a straight line segment. It will be shown that for any knot or link type $k$, there is a finite number $R(k)$ such that every linear embedding of the complete graph ${K_n}$ with at least $R(k)$ vertices $(n \geqslant R(k))$ in ${{\mathbf {R}}^3}$ contains a knot or link equivalent to $k$.

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Additional Information
Keywords:
Knots,
links,
spatial graphs,
Ramsey theory
Article copyright:
© Copyright 1991
American Mathematical Society