0,1

Foisy et al p. 17: "Unlike in R3, where there are simple arguments showing that there are no minor-minimal intrinsically linked graphs with connectivity 0, 1, or 2, such graphs exist in projective space. Using careful combinatorics, one can show that there are 21 disconnected graphs [i.e. with 2-connectivity], 91 graphs with 1-connectivity and 469 graphs with 2-connectivity which are minor-minimal intrinsically linked in RP^3."

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, Howards, Lawrence and Mellor]. 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 RP3 and prove that K_7 minus any two edges is also minor-minimal intrinsically linked. In all, 594 graphs are shown to be minor-minimal intrinsically linked in

E. Flapan, H. Howards, D. Lawrence and B. Mellor. Intrinsic linking and knotting of graphs in arbitrary 3-manifolds. Algebraic and Geometric Topology, 6:1025{1035, 2006.

Joel Foisy, Jason Bustamante, Jared Federman, Kenji Kozai, Kevin Matthews, Kristen McNamara, Emily Stark, Kirsten Trickey, Intrinsically Linked Graphs in Projective Space, Sep 2, 2008.

Sequence in context: A158540 A020248 A065827 this_sequence A119109 A144856 A065522

Adjacent sequences: A143840 A143841 A143842 this_sequence A143844 A143845 A143846

bref,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 03 2008