#### Volume 9, issue 3 (2009)

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Intrinsically linked graphs in projective space

### Jason Bustamante, Jared Federman, Joel Foisy, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark and Kirsten Trickey

Algebraic & Geometric Topology 9 (2009) 1255–1274
##### 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 $ℝ{P}^{3}$. We fully characterize such graphs with connectivity $0$, $1$ and $2$. We also show that only one Petersen-family graph is intrinsically linked in $ℝ{P}^{3}$ 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 $ℝ{P}^{3}$.