A143843 Number of graphs with n-connectivity which are minor-minimal intrinsically linked in the 3-dimensional real projective space RP^3.

21, 91, 469

Offset

0,1

Comments

Foisy et al. p. 17: "Unlike 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

Links

Table of n, a(n) for n=0..2.

E. Flapan, H. Howards, D. Lawrence and B. Mellor, Intrinsic linking and knotting of graphs in arbitrary 3-manifolds, Algebraic and Geometric Topology, 6 (2006) 1025-1036.

Joel Foisy, Jason Bustamante, Jared Federman, Kenji Kozai, Kevin Matthews, Kristen McNamara, Emily Stark and Kirsten Trickey, Intrinsically Linked Graphs in Projective Space, arXiv:0809.0454 [math.GT]

Crossrefs

Sequence in context: A065827 A318036 A326164 * A119109 A254603 A144856

Adjacent sequences: A143840 A143841 A143842 * A143844 A143845 A143846

Keyword

bref,nonn

Author

Jonathan Vos Post, Sep 03 2008

Status

approved