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.
Citation
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
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