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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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

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.

RP^3, projective, graph, link
Mathematical Subject Classification 2000
Primary: 05C10
Secondary: 57M15
Received: 2 September 2008
Revised: 4 April 2009
Accepted: 5 April 2009
Published: 1 July 2009
Jason Bustamante
Department of Mathematical Sciences
Montana Tech of The University of Montana
1300 West Park Street
Butte, MT 59701
Jared Federman
Department of Mathematics
SUNY Potsdam
Potsdam, NY 13676
Joel Foisy
Department of Mathematics
SUNY Potsdam
Potsdam, NY 13676
Kenji Kozai
Department of Mathematics
Stanford University
450 Serra Mall
Building 380
Stanford, CA 94305
Kevin Matthews
Department of Mathematics
SUNY Potsdam
Potsdam, NY 13676
Kristin McNamara
Department of Mathematics and Statistics
James Madison University
305 Roop Hall MSC 1911
Harrisonburg, VA 22807
Emily Stark
Department of Mathematics
Pomona College
610 North College Avenue
Claremont, CA 91711
Kirsten Trickey
Department of Mathematics
Clarkson University
8 Clarkson Avenue
Potsdam, NY 13699