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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Ramsey theorems for knots, links and spatial graphs
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by Seiya Negami PDF
Trans. Amer. Math. Soc. 324 (1991), 527-541 Request permission

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
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 527-541
  • MSC: Primary 57M25; Secondary 05C10
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1069741-9
  • MathSciNet review: 1069741