## Algebraic & Geometric Topology

### Exactly fourteen intrinsically knotted graphs have $21$ edges

#### Abstract

Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least $21$ edges. Also it is known that $K7$ and the thirteen graphs obtained from $K7$ by $∇Y$ moves are intrinsically knotted graphs with $21$ edges. We prove that these 14 graphs are the only intrinsically knotted graphs with $21$ edges.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3305-3322.

Dates
Revised: 13 March 2015
Accepted: 24 March 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841068

Digital Object Identifier
doi:10.2140/agt.2015.15.3305

Mathematical Reviews number (MathSciNet)
MR3450762

Zentralblatt MATH identifier
1333.57015

Keywords
intrinsically knotted graph

#### Citation

Lee, Minjung; Kim, Hyoungjun; Lee, Hwa Jeong; Oh, Seungsang. Exactly fourteen intrinsically knotted graphs have $21$ edges. Algebr. Geom. Topol. 15 (2015), no. 6, 3305--3322. doi:10.2140/agt.2015.15.3305. https://projecteuclid.org/euclid.agt/1510841068

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