Vol. 9, No. 5, 2016

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ISSN: 1944-4184 (e-only)
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New examples of Brunnian theta graphs

Byoungwook Jang, Anna Kronaeur, Pratap Luitel, Daniel Medici, Scott A. Taylor and Alexander Zupan

Vol. 9 (2016), No. 5, 857–875
Abstract

The Kinoshita graph is the most famous example of a Brunnian theta graph, a nontrivial spatial theta graph with the property that removing any edge yields an unknot. We produce a new family of diagrams of spatial theta graphs with the property that removing any edge results in the unknot. The family is parameterized by a certain subgroup of the pure braid group on four strands. We prove that infinitely many of these diagrams give rise to distinct Brunnian theta graphs.

Keywords
spatial graph, almost unknotted graph, Brunnian, theta graph, theta curve, rational tangle
Mathematical Subject Classification 2010
Primary: 57M25
Milestones
Received: 17 August 2015
Revised: 20 October 2015
Accepted: 22 October 2015
Published: 25 August 2016

Communicated by Joel Foisy
Authors
Byoungwook Jang
Department of Mathematics and Statistics
Colby College c/o Scott Taylor
Waterville, ME 04901-8858
United States
Anna Kronaeur
Department of Mathematics and Statistics
Colby College
Waterville, ME 04901-8858
United States
Pratap Luitel
Department of Mathematics and Statistics
Colby College c/o Scott Taylor
Waterville, ME 04901-8858
United States
Daniel Medici
Department of Mathematics and Statistics
Colby College
Waterville, ME 04901-8858
United States
Scott A. Taylor
Department of Mathematics and Statistics
Colby College
5832 Mayflower Hill
Waterville, ME 04901-8858
United States
Alexander Zupan
Department of Mathematics
University of Nebraska-Lincoln
1400 R Street
Lincoln, NE 68588
United States