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

Yuta Akimoto; Kouki Taniyama

doi:10.1142/S0218216520500959

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

Yuta Akimoto, Kouki Taniyama^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	2050095
Journal	Journal of Knot Theory and its Ramifications
Volume	29
Issue number	14
DOIs	https://doi.org/10.1142/S0218216520500959
Publication status	Published - 2020 Dec

Keywords

Knot
crossing number
knotted projection
spatial graph
trivializable graph
unknotting number

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216520500959

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title = "Unknotting numbers and crossing numbers of spatial embeddings of a planar graph",

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.",

keywords = "Knot, crossing number, knotted projection, spatial graph, trivializable graph, unknotting number",

author = "Yuta Akimoto and Kouki Taniyama",

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AU - Taniyama, Kouki

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N2 - 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.

AB - 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.

KW - Knot

KW - crossing number

KW - knotted projection

KW - spatial graph

KW - trivializable graph

KW - unknotting number

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JF - Journal of Knot Theory and its Ramifications

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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