## Tokyo Journal of Mathematics

### Intrinsically $n$-linked Complete Graphs

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 32, Number 1 (2009), 113-125.

Dates
First available in Project Euclid: 7 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1249648413

Digital Object Identifier
doi:10.3836/tjm/1249648413

Mathematical Reviews number (MathSciNet)
MR2541160

Zentralblatt MATH identifier
1184.05026

#### Citation

DRUMMOND-COLE, Gabriel C.; O'DONNOL, Danielle. Intrinsically $n$-linked Complete Graphs. Tokyo J. Math. 32 (2009), no. 1, 113--125. doi:10.3836/tjm/1249648413. https://projecteuclid.org/euclid.tjm/1249648413

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