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

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 $ℝP^3$, the graph $K_{10}$ is intrinsically triple-linked in $ℝP^3$.