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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Exactly fourteen intrinsically knotted graphs have $21$ edges

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

Algebraic & Geometric Topology 15 (2015) 3305–3322
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.

Keywords
intrinsically knotted, graph
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 9 June 2014
Revised: 13 March 2015
Accepted: 24 March 2015
Published: 12 January 2016
Authors
Minjung Lee
Department of Mathematics
Korea University
Anam-dong
Sungbuk-ku
Seoul 136-701
South Korea
Hyoungjun Kim
Department of Mathematics
Korea University
Anam-dong
Sungbuk-ku
Seoul 136-701
South Korea
Hwa Jeong Lee
Department of Mathematical Sciences
KAIST
291 Daehak-ro
Yuseong-gu
Daejeon 305-701
South Korea
Seungsang Oh
Department of Mathematics
Korea University
Anam-dong
Sungbuk-ku
Seoul 136-701
South Korea