## Involve: A Journal of Mathematics

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

### New examples of Brunnian theta graphs

#### 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.

#### Article information

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

Dates
Revised: 20 October 2015
Accepted: 22 October 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371075

Digital Object Identifier
doi:10.2140/involve.2016.9.857

Mathematical Reviews number (MathSciNet)
MR3541985

Zentralblatt MATH identifier
1346.57010

#### Citation

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. https://projecteuclid.org/euclid.involve/1511371075

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