#### Vol. 10, No. 1, 2017

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Intrinsically triple-linked graphs in $\mathbb{R}P^3$

### Jared Federman, Joel Foisy, Kristin McNamara and Emily Stark

Vol. 10 (2017), No. 1, 1–20
##### Abstract

Flapan, Naimi and Pommersheim (2001) showed that every spatial embedding of ${K}_{10}$, the complete graph on ten vertices, contains a nonsplit three-component link; that is, ${K}_{10}$ is intrinsically triple-linked in ${ℝ}^{3}$. The work of Bowlin and Foisy (2004) and Flapan, Foisy, Naimi, and Pommersheim (2001) extended the list of known intrinsically triple-linked graphs in ${ℝ}^{3}$ to include several other families of graphs. In this paper, we will show that while some of these graphs can be embedded 3-linklessly in $ℝ{P}^{3}$, the graph ${K}_{10}$ is intrinsically triple-linked in $ℝ{P}^{3}$.

##### Keywords
intrinsically linked, graphs embedded in real projective space
Primary: 57M27