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Erica Flapan,
Kenji Kozai, and
Ryo Nikkuni
Stick number of non-paneled knotless spatial graphs
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| Published: |
July 29, 2020. |
| Keywords: |
Non-paneled knotless spatial graphs, stick embeddings of graphs,
metalloproteins, Mobius ladders, ravels, K3,3, K4, K5. |
| Subject: |
57M15, 57K10, 05C10, 92C40, 92E10. |
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Abstract
We show that the minimum number of sticks required to construct a non-paneled knotless embedding of K4
is 8 and of K5 is 12 or 13. We use our results about K4 to show that the probability that a
random linear embedding of K3,3 in a cube is in the form of a Mobius ladder is 0.97380 ± 0.00003, and
offer this as a possible explanation for why K3,3 subgraphs of metalloproteins occur primarily in this form.
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| Acknowledgements
The first author was supported in part by NSF Grant DMS-1607744. The third author was supported by JSPS KAKENHI Grant Number JP15K04881.
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| Author information
Erica Flapan:
Department of Mathematics
610 N. College Ave.
Pomona College
Claremont, CA 91711, USA
elf04747@pomona.edu
Kenji Kozai:
Department of Mathematics
Rose-Hulman Institute of Technology
5500 Wabash Ave., Terre Haute, IN 47803, USA
kozai@rose-hulman.edu
Ryo Nikkuni:
Department of Mathematics
Tokyo Woman's Christian University
2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
nick@lab.twcu.ac.jp
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