Geodesic
Exactly fourteen intrinsically knotted graphs have 21 edges
Lee, Minjung1 ; Kim, Hyoungjun1 ; Lee, Hwa Jeong2 ; Oh, Seungsang1
1Department of Mathematics, Korea University, Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea
2Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea
Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3305-3322
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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.

DOI : 10.2140/agt.2015.15.3305
Classification : 57M25, 57M27
Keywords: intrinsically knotted, graph

Lee, Minjung  1   ; Kim, Hyoungjun  1   ; Lee, Hwa Jeong  2   ; Oh, Seungsang  1

1 Department of Mathematics, Korea University, Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea
2 Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, South Korea 
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Lee, Minjung; Kim, Hyoungjun; Lee, Hwa Jeong; Oh, Seungsang. Exactly fourteen intrinsically knotted graphs have 21 edges. Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3305-3322. doi: 10.2140/agt.2015.15.3305

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