Knot-inevitable projections of planar graphs

Kouki Taniyama, Tatsuya Tsukamoto

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2,n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

Original languageEnglish
Pages (from-to)877-883
Number of pages7
JournalJournal of Knot Theory and its Ramifications
Volume5
Issue number6
Publication statusPublished - 1996 Dec
Externally publishedYes

Fingerprint

Spatial Graph
Planar graph
Knot
Projection
Torus knot
Odd number
Subgraph
Graph in graph theory

Keywords

  • Knot
  • Planar graph
  • Regular projection

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Knot-inevitable projections of planar graphs. / Taniyama, Kouki; Tsukamoto, Tatsuya.

In: Journal of Knot Theory and its Ramifications, Vol. 5, No. 6, 12.1996, p. 877-883.

Research output: Contribution to journalArticle

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