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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

intrinsically knotted graph


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.

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