Exactly fourteen intrinsically knotted graphs have 21 edges

Minjung Lee; Hyoungjun Kim; Hwa Jeong Lee; Seungsang Oh

doi:10.2140/agt.2015.15.3305

Exactly fourteen intrinsically knotted graphs have 21 edges

Minjung Lee, Hyoungjun Kim, Hwa Jeong Lee, Seungsang Oh

Department of Mathematics Education

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

11 Scopus citations

Abstract

Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K₇ and the thirteen graphs obtained from K₇ by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

Original language	English
Pages (from-to)	3305-3322
Number of pages	18
Journal	Algebraic and Geometric Topology
Volume	15
Issue number	6
DOIs	https://doi.org/10.2140/agt.2015.15.3305
State	Published - 12 Jan 2016

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10.2140/agt.2015.15.3305

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title = "Exactly fourteen intrinsically knotted graphs have 21 edges",

abstract = "Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.",

author = "Minjung Lee and Hyoungjun Kim and Lee, \{Hwa Jeong\} and Seungsang Oh",

year = "2016",

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T1 - Exactly fourteen intrinsically knotted graphs have 21 edges

AU - Lee, Minjung

AU - Kim, Hyoungjun

AU - Lee, Hwa Jeong

AU - Oh, Seungsang

PY - 2016/1/12

Y1 - 2016/1/12

N2 - Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

AB - Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by ∇Y moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

UR - https://www.scopus.com/pages/publications/84957084716

U2 - 10.2140/agt.2015.15.3305

DO - 10.2140/agt.2015.15.3305

M3 - Article

AN - SCOPUS:84957084716

SN - 1472-2747

VL - 15

SP - 3305

EP - 3322

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 6

ER -

Exactly fourteen intrinsically knotted graphs have 21 edges

Abstract

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