Vol. 10, No. 1, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Intrinsically triple-linked graphs in $\mathbb{R}P^3$

Jared Federman, Joel Foisy, Kristin McNamara and Emily Stark

Vol. 10 (2017), No. 1, 1–20
Abstract

Flapan, Naimi and Pommersheim (2001) showed that every spatial embedding of K10, the complete graph on ten vertices, contains a nonsplit three-component link; that is, K10 is intrinsically triple-linked in 3. The work of Bowlin and Foisy (2004) and Flapan, Foisy, Naimi, and Pommersheim (2001) extended the list of known intrinsically triple-linked graphs in 3 to include several other families of graphs. In this paper, we will show that while some of these graphs can be embedded 3-linklessly in P3, the graph K10 is intrinsically triple-linked in P3.

Keywords
intrinsically linked, graphs embedded in real projective space
Mathematical Subject Classification 2010
Primary: 57M27
Milestones
Received: 16 February 2009
Revised: 31 October 2015
Accepted: 31 December 2015
Published: 11 October 2016

Communicated by Kenneth S. Berenhaut
Authors
Jared Federman
Department of Mathematics
SUNY Potsdam
Potsdam, NY 13676
United States
Joel Foisy
Department of Mathematics
SUNY Potsdam
Potsdam, NY 13676
United States
Kristin McNamara
Department of Mathematics and Statistics
James Madison University
Harrisonburg, VA 22807
United States
Emily Stark
Department of Mathematics
Pomona College
Claremont, CA 91711
United States