A large complete graph in a space contains a link with large link invariant

Minori Shirai; Kouki Taniyama

doi:10.1142/S0218216503002858

A large complete graph in a space contains a link with large link invariant

Minori Shirai^*, Kouki Taniyama

^*Corresponding author for this work

School of Education

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

2 Citations (Scopus)

Abstract

Let k be a non-negative integer. Then any embedding of the complete graph on 6 · 2^k vertices into a three-space contains a two-component link with the absolute value of its linking number greater than or equal to 2^k. Let j be a non-negative integer. Then any embedding of the complete graph on 48 · 2^k vertices into a three-space contains a knot with the absolute value of the second coefficient of its Conway polynomial greater than or equal to 2^2j.

Original language	English
Pages (from-to)	915-919
Number of pages	5
Journal	Journal of Knot Theory and its Ramifications
Volume	12
Issue number	7
DOIs	https://doi.org/10.1142/S0218216503002858
Publication status	Published - 2003 Nov 1

Keywords

Complete graph
Intrinsic knotting
Intrinsic linking
Linking number
Second coefficient of Conway polynomial
Spatial graph

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216503002858

Cite this

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AU - Taniyama, Kouki

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AB - Let k be a non-negative integer. Then any embedding of the complete graph on 6 · 2k vertices into a three-space contains a two-component link with the absolute value of its linking number greater than or equal to 2k. Let j be a non-negative integer. Then any embedding of the complete graph on 48 · 2k vertices into a three-space contains a knot with the absolute value of the second coefficient of its Conway polynomial greater than or equal to 22j.

KW - Complete graph

KW - Intrinsic knotting

KW - Intrinsic linking

KW - Linking number

KW - Second coefficient of Conway polynomial

KW - Spatial graph

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A large complete graph in a space contains a link with large link invariant

Abstract

Keywords

ASJC Scopus subject areas

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