Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams

Sungjong No, Seungsang Oh, Hyungkee Yoo

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a bisected vertex leveling of a plane graph. Using this planar embedding, we present elementary proofs of the well-known upper bounds in terms of the minimal crossing number on braid index b(L) and arc index α(L) for any knot or non-split link L, which are b(L) ≤ 1 2c(L) + 1 and α(L) ≤ c(L) + 2. We also find a quadratic upper bound of the minimal crossing number of delta diagrams of L.

Original languageEnglish
Article number1850044
JournalJournal of Knot Theory and its Ramifications
Volume27
Issue number8
DOIs
Publication statusPublished - 2018 Jul 1

Keywords

  • Knot
  • arc index
  • braid index
  • delta diagram
  • link

ASJC Scopus subject areas

  • Algebra and Number Theory

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