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

Minori Shirai, Kouki Taniyama

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)915-919
Number of pages5
JournalJournal of Knot Theory and its Ramifications
Volume12
Issue number7
DOIs
Publication statusPublished - 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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