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Intrinsically linked
graphs in projective space
Jason Bustamante, Jared Federman, Joel Foisy, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark and Kirsten Trickey |
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Algebraic & Geometric Topology 9 (2009) 1255–1274
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Abstract |
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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 . We fully characterize such graphs with connectivity , and . We also show that only one Petersen-family graph is intrinsically linked in and prove that minus any two edges is also minor-minimal intrinsically linked. In all, graphs are shown to be minor-minimal intrinsically linked in . |
Keywords
RP^3, projective, graph, link
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Mathematical Subject Classification 2000
Primary: 05C10
Secondary: 57M15
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References |
Publication
Received: 2 September 2008
Revised: 4 April 2009
Accepted: 5 April 2009
Published: 1 July 2009
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Authors |
| Jason Bustamante | |
| Department of Mathematical
Sciences Montana Tech of The University of Montana 1300 West Park Street Butte, MT 59701 USA |
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| Jared Federman | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
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| Joel Foisy | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
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| http://www2.potsdam.edu/foisyjs/ | |
| Kenji Kozai | |
| Department of Mathematics Stanford University 450 Serra Mall Building 380 Stanford, CA 94305 USA |
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| http://math.stanford.edu/~kkozai/ | |
| Kevin Matthews | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
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| Kristin McNamara | |
| Department of Mathematics and
Statistics James Madison University 305 Roop Hall MSC 1911 Harrisonburg, VA 22807 USA |
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| Emily Stark | |
| Department of Mathematics Pomona College 610 North College Avenue Claremont, CA 91711 USA |
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| Kirsten Trickey | |
| Department of Mathematics Clarkson University 8 Clarkson Avenue Potsdam, NY 13699 USA |
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