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Hiroka Hashimoto and Ryo Nikkuni
Conway-Gordon type theorem for the complete four-partite graph K3,3,1,1 view print
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| Published: |
May 24, 2014 |
| Keywords: |
Spatial graph, Intrinsic knottedness, Rectilinear spatial graph |
| Subject: |
Primary 57M15; Secondary 57M25 |
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Abstract
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph K3,3,1,1 in terms of the square of the linking number and the second coefficient of the Conway polynomial. As an application, we show that every rectilinear spatial K3,3,1,1 contains a nontrivial Hamiltonian knot.
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| Acknowledgements
The second author was partially supported by Grant-in-Aid for Young Scientists (B) (No. 21740046), Japan Society for the Promotion of Science.
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| Author information
Hiroka Hashimoto:
Division of Mathematics, Graduate School of Science, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
etiscatbird@yahoo.co.jp
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
nick@lab.twcu.ac.jp
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