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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ramsey theorems for knots, links and spatial graphs

Author: Seiya Negami
Journal: Trans. Amer. Math. Soc. 324 (1991), 527-541
MSC: Primary 57M25; Secondary 05C10
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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Keywords: Knots, links, spatial graphs, Ramsey theory
Article copyright: © Copyright 1991 American Mathematical Society

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