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On intrinsically
knotted or completely 3-linked graphs
Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama and Akiko Yamazaki |
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Vol. 252 (2011), No. 2, 407–425
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Abstract |
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We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of △Y-exchanges and Y△-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph. |
Keywords
spatial graph, intrinsic knottedness, △Y-exchange,
Y△-exchange
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Mathematical Subject Classification 2000
Primary: 57M15
Secondary: 57M25
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Milestones
Received: 10 August 2010
Revised: 20 January 2011
Accepted: 20 January 2011
Published: 29 October 2011
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Authors |
| Ryo Hanaki | |
| Department of Mathematics Nara University of Education Takabatake Nara 630-8305 Japan |
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| Ryo Nikkuni | |
| Department of Mathematics, School of
Arts and Sciences Tokyo Woman’s Christian University 2-6-1 Zempukuji, Suginami-ku Tokyo 167-8585 Japan |
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| Kouki Taniyama | |
| Department of Mathematics, School of
Education Waseda University Nishi-Waseda 1-6-1, Shinjuku-ku Tokyo 169-8050 Japan |
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| Akiko Yamazaki | |
| Division of Mathematics, Graduate
School of Science Tokyo Woman’s Christian University 2-6-1 Zempukuji, Suginami-ku Tokyo 167-8585 Japan |
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