Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 5 (2016), 857-875.

New examples of Brunnian theta graphs

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

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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.

Article information

Involve, Volume 9, Number 5 (2016), 857-875.

Received: 17 August 2015
Revised: 20 October 2015
Accepted: 22 October 2015
First available in Project Euclid: 22 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

spatial graph almost unknotted graph Brunnian theta graph theta curve rational tangle


Jang, Byoungwook; Kronaeur, Anna; Luitel, Pratap; Medici, Daniel; Taylor, Scott; Zupan, Alexander. New examples of Brunnian theta graphs. Involve 9 (2016), no. 5, 857--875. doi:10.2140/involve.2016.9.857.

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