Algebraic & Geometric Topology

Exactly fourteen intrinsically knotted graphs have $21$ edges

Minjung Lee, Hyoungjun Kim, Hwa Jeong Lee, and Seungsang Oh

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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
Received: 9 June 2014
Revised: 13 March 2015
Accepted: 24 March 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

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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References

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