Intrinsically $n$-linked Complete Graphs
Gabriel C. DRUMMOND-COLE and Danielle O'DONNOL
Source: Tokyo J. of Math.
Volume 32, Number 1
(2009), 113-125.
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tjm/1249648413
Digital Object Identifier: doi:10.3836/tjm/1249648413
Zentralblatt MATH identifier:
05604239
Mathematical Reviews number (MathSciNet):
MR2541160
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