Intrinsically Linked Graphs in Projective Space

Joel Foisy; Jason Bustamante; Jared Federman; Kenji Kozai; Kevin Matthews; Kristen McNamara; Emily Stark; Kirsten Trickey

doi:10.2140/agt.2009.9.1255

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arXiv · 0809.0454

Intrinsically Linked Graphs in Projective Space

Joel Foisy·Jason Bustamante·Jared Federman·Kenji Kozai·Kevin Matthews·Kristen McNamara·Emily Stark·Kirsten Trickey

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Abstract

We examine graphs that contain a non-trivial link in every embedding into real projective space, using a weaker notion of unlink than was used by Flapan, et al. We call such graphs intrinsically linked in projective space. We fully characterize such graphs with connectivity 0,1 and 2. We also show that only one Petersen-family graph is intrinsically linked in projective space and prove that K7 minus any two edges is also minor-minimal intrinsically linked. In all, 594 graphs are shown to be minor-minimal intrinsically linked in projective space.

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Joel Foisy, Jason Bustamante, Jared Federman, Kenji Kozai, Kevin Matthews, Kristen McNamara, Emily Stark, Kirsten Trickey. 2008-09-02. Intrinsically Linked Graphs in Projective Space. https://doi.org/10.2140/agt.2009.9.1255

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