|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Intrinsically linked graphs in projective space
Jason Bustamante, Jared Federman, Joel Foisy, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark and Kirsten Trickey |
|
Algebraic & Geometric Topology 9 (2009) 1255–1274 |
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 RP3. 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 K7 minus any two edges is also minor-minimal intrinsically linked. In all, 597 graphs are shown to be minor-minimal intrinsically linked in RP3. |
KeywordsRP^3, projective, graph, link |
Mathematical Subject ClassificationPrimary: 05C10 Secondary: 57M15 |
References |
PublicationReceived: 2 September 2008 |
Authors |
| Jason Bustamante | |
| Department of Mathematical
Sciences Montana Tech of The University of Montana 1300 West Park Street Butte, MT 59701 USA |
|
| Jared Federman | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
|
| Joel Foisy | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
|
| http://www2.potsdam.edu/foisyjs/ | |
| Kenji Kozai | |
| Department of Mathematics Stanford University 450 Serra Mall Building 380 Stanford, CA 94305 USA |
|
| http://math.stanford.edu/~kkozai/ | |
| Kevin Matthews | |
| Department of Mathematics SUNY Potsdam Potsdam, NY 13676 USA |
|
| Kristin McNamara | |
| Department of Mathematics and
Statistics James Madison University 305 Roop Hall MSC 1911 Harrisonburg, VA 22807 USA |
|
| Emily Stark | |
| Department of Mathematics Pomona College 610 North College Avenue Claremont, CA 91711 USA |
|
| Kirsten Trickey | |
| Department of Mathematics Clarkson University 8 Clarkson Avenue Potsdam, NY 13699 USA |
|
