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A143843
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Number of graphs with n-connectivity which are minor-minimal intrinsically linked in the 3-dimensional real projective space RP^3.
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0
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OFFSET
| 0,1
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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
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LINKS
| 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]
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CROSSREFS
| Sequence in context: A203173 A194532 A065827 * A119109 A144856 A065522
Adjacent sequences: A143840 A143841 A143842 * A143844 A143845 A143846
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KEYWORD
| bref,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 03 2008
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EXTENSIONS
| Replaced link to cached arXiv URL by link to the abstract - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 01 2010
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