On intrinsically knotted or completely 3-linked graphs

Ryo Hanaki; Ryo Nikkuni; Kouki Taniyama; Akiko Yamazaki

doi:10.2140/pjm.2011.252.407

On intrinsically knotted or completely 3-linked graphs

Ryo Hanaki^*, Ryo Nikkuni, Kouki Taniyama, Akiko Yamazaki

^*Corresponding author for this work

School of Education

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

15 Citations (Scopus)

Abstract

We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of ΔY-exchanges and YΔ-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

Original language	English
Pages (from-to)	407-425
Number of pages	19
Journal	Pacific Journal of Mathematics
Volume	252
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2011.252.407
Publication status	Published - 2011

Keywords

Intrinsic knottedness
Spatial graph
YΔ-exchange
ΔY-exchange

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2011.252.407

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AB - We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of ΔY-exchanges and YΔ-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

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KW - Spatial graph

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KW - ΔY-exchange

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On intrinsically knotted or completely 3-linked graphs

Abstract

Keywords

ASJC Scopus subject areas

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