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June 2009 Intrinsically $n$-linked Complete Graphs
Gabriel C. DRUMMOND-COLE, Danielle O'DONNOL
Tokyo J. Math. 32(1): 113-125 (June 2009). DOI: 10.3836/tjm/1249648413

Abstract

In this paper we examine the question: given $n>1$, find a function $f:\mathbf{N}\rightarrow \mathbf{N}$ where $m=f(n)$ is the smallest integer such that $K_m$ is intrinsically $n$-linked. We prove that for $n>1$, every embedding of $K_{\lfloor \frac{7}{2}n\rfloor}$ in $\mathbf{R}^3$ contains a non-splittable link of $n$ components. We also prove an asymptotic result, that there exists a function $f(n)$ such that $ \lim_{n\to \infty}\frac{f(n)}{n}=3$ and, for every $n,$ $K_{f(n)}$ is intrinsically $n$-linked.

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Gabriel C. DRUMMOND-COLE. Danielle O'DONNOL. "Intrinsically $n$-linked Complete Graphs." Tokyo J. Math. 32 (1) 113 - 125, June 2009. https://doi.org/10.3836/tjm/1249648413

Information

Published: June 2009
First available in Project Euclid: 7 August 2009

zbMATH: 1184.05026
MathSciNet: MR2541160
Digital Object Identifier: 10.3836/tjm/1249648413

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

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Vol.32 • No. 1 • June 2009
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