Intrinsically triple-linked graphs in \(\mathbb{R}P^3\) (Q329815)

A graph is said to be intrinsically triple-linked in a 3-dimensional topological space \(X\), if every embedding of the graph into \(X\) contains a nonsplittable link of three components. The authors show that the complete graph \(K_{10}\) has the property in \(\mathbb{R}P^3\). Additionally some graphs which are intrinsically triple-linked in \(\mathbb{R}^3\) are shown not to have the property in \(\mathbb{R}P^3\).