Intrinsically linked graphs in projective space
Jason Bustamante, Jared Federman, Joel Foisy, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark, Kirsten Trickey · Algebraic & Geometric Topology · 2009
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 [5].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 minorminimal intrinsically linked.In all, 597 graphs are shown to be minor-minimal intrinsically linked in RP 3 .