Intrinsically triple-linked graphs in ℝP3

Federman, Jared; Foisy, Joel; McNamara, Kristin; Stark, Emily

doi:10.2140/involve.2017.10.1

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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

DOI: 10.2140/involve.2017.10.1

Abstract

Flapan, Naimi and Pommersheim (2001) showed that every spatial embedding of $K_{10}$ , the complete graph on ten vertices, contains a nonsplit three-component link; that is, $K_{10}$ is intrinsically triple-linked in $ℝ^{3}$ . The work of Bowlin and Foisy (2004) and Flapan, Foisy, Naimi, and Pommersheim (2001) extended the list of known intrinsically triple-linked graphs in $ℝ^{3}$ 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 $ℝ P^{3}$ , the graph $K_{10}$ is intrinsically triple-linked in $ℝ P^{3}$ .

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

Vol. 10, No. 1, 2017