Intrinsically linked graphs in projective space

Abstract

We examine graphs that contain a nontrivial link in every embedding into real projective space, using a weaker notion of unlink than was used in Flapan, et al [Algebr. Geom. Topol. 6 (2006) 1025–1035]. We call such graphs intrinsically linked in $ℝP^3$. We fully characterize such graphs with connectivity $0$, $1$ and $2$. We also show that only one Petersen-family graph is intrinsically linked in $ℝP^3$ and prove that $K_7$ minus any two edges is also minor-minimal intrinsically linked. In all, $597$ graphs are shown to be minor-minimal intrinsically linked in $ℝP^3$.