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2009 Intrinsically linked graphs in projective space
Jason Bustamante, Jared Federman, Joel Foisy, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark, Kirsten Trickey
Algebr. Geom. Topol. 9(3): 1255-1274 (2009). DOI: 10.2140/agt.2009.9.1255

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, et al [Algebr. Geom. Topol. 6 (2006) 1025–1035]. We call such graphs intrinsically linked in P3. We fully characterize such graphs with connectivity 0, 1 and 2. We also show that only one Petersen-family graph is intrinsically linked in P3 and prove that K7 minus any two edges is also minor-minimal intrinsically linked. In all, 597 graphs are shown to be minor-minimal intrinsically linked in P3.

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Jason Bustamante. Jared Federman. Joel Foisy. Kenji Kozai. Kevin Matthews. Kristin McNamara. Emily Stark. Kirsten Trickey. "Intrinsically linked graphs in projective space." Algebr. Geom. Topol. 9 (3) 1255 - 1274, 2009. https://doi.org/10.2140/agt.2009.9.1255

Information

Received: 2 September 2008; Revised: 4 April 2009; Accepted: 5 April 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1182.05039
MathSciNet: MR2520399
Digital Object Identifier: 10.2140/agt.2009.9.1255

Subjects:
Primary: 05C10
Secondary: 57M15

Keywords: graph, link, projective, RP^3

Rights: Copyright © 2009 Mathematical Sciences Publishers

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