%I A143843
%S A143843 21,91,469
%N A143843 Number of graphs with n-connectivity which are minor-minimal intrinsically 
               linked in the 3-dimensional real projective space RP^3.
%C A143843 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."
%C A143843 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
%D A143843 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.
%H A143843 Joel Foisy, Jason Bustamante, Jared Federman, Kenji Kozai, Kevin Matthews, 
               Kristen McNamara, Emily Stark, Kirsten Trickey, <a href="http://arxiv.org/
               PS_cache/arxiv/pdf/0809/0809.0454v1.pdf">Intrinsically Linked Graphs 
               in Projective Space</a>, Sep 2, 2008.
%Y A143843 Sequence in context: A158540 A020248 A065827 this_sequence A119109 A144856 
               A065522
%Y A143843 Adjacent sequences: A143840 A143841 A143842 this_sequence A143844 A143845 
               A143846
%K A143843 bref,nonn
%O A143843 0,1
%A A143843 Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 03 2008