Unknotting numbers and crossing numbers of spatial embeddings of a planar graph

Yuta Akimoto; Kouki Taniyama

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arXiv · 2010.05245

Unknotting numbers and crossing numbers of spatial embeddings of a planar graph

Yuta Akimoto·Kouki Taniyama

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Abstract

It is known that the unknotting number $u(L)$ of a link $L$ is less than or equal to half the crossing number $c(L)$ of $L$. We show that there are a planar graph $G$ and its spatial embedding $f$ such that the unknotting number $u(f)$ of $f$ is greater than half the crossing number $c(f)$ of $f$. We study relations between unknotting number and crossing number of spatial embedding of a planar graph in general.

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Yuta Akimoto, Kouki Taniyama. 2020-10-11. Unknotting numbers and crossing numbers of spatial embeddings of a planar graph. https://arxiv.org/abs/2010.05245

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