

A143843


Number of graphs with nconnectivity which are minorminimal intrinsically linked in the 3dimensional real projective space RP^3.


0




OFFSET

0,1


COMMENTS

Foisy et al. p. 17: "Unlike R3, where there are simple arguments showing that there are no minorminimal 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 2connectivity], 91 graphs with 1connectivity and 469 graphs with 2connectivity which are minorminimal 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 Petersenfamily graph is intrinsically linked in RP3 and prove that K_7 minus any two edges is also minorminimal intrinsically linked. In all, 594 graphs are shown to be minorminimal 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 3manifolds, Algebraic and Geometric Topology, 6 (2006) 10251036.
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



