Stick number of non-paneled knotless spatial graphs

Erica Flapan; Kenji Kozai; Ryo Nikkuni

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arXiv · 1909.01223

Stick number of non-paneled knotless spatial graphs

Erica Flapan·Kenji Kozai·Ryo Nikkuni

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Abstract

We show that the minimum number of sticks required to construct a non-paneled knotless embedding of $K_4$ is 9 and of $K_5$ is 12 or 13. We use our results about $K_4$ to show that the probability that a random linear embedding of $K_{3,3}$ in a cube is in the form of a M\"{o}bius ladder is $0.97380\pm 0.00003$, and offer this as a possible explanation for why $K_{3,3}$ subgraphs of metalloproteins occur primarily in this form.

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Erica Flapan, Kenji Kozai, Ryo Nikkuni. 2019-09-03. Stick number of non-paneled knotless spatial graphs. https://arxiv.org/abs/1909.01223

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