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

Sungjong No, Seung Sang Oh, Hyungkee Yoo

Research output: Contribution to journal › Article

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 (Formula presented.) and arc index (Formula presented.) for any knot or non-split link (Formula presented.), which are (Formula presented.) and (Formula presented.). We also find a quadratic upper bound of the minimal crossing number of delta diagrams of (Formula presented.).

Original languageEnglish
JournalJournal of Knot Theory and its Ramifications
DOIs
Publication statusAccepted/In press - 2018 Jun 8

Fingerprint

Plane Graph
Braid
Arc of a curve
Diagram
Vertex of a graph
Crossing number
Upper bound
Knot

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Bisected vertex leveling of plane graphs : Braid index, arc index and delta diagrams. / No, Sungjong; Oh, Seung Sang; Yoo, Hyungkee.

In: Journal of Knot Theory and its Ramifications, 08.06.2018.

Research output: Contribution to journal › Article

No, S, Oh, SS & Yoo, H 2018, 'Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams', Journal of Knot Theory and its Ramifications. https://doi.org/10.1142/S021821651850044X
No S, Oh SS, Yoo H. Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams. Journal of Knot Theory and its Ramifications. 2018 Jun 8. https://doi.org/10.1142/S021821651850044X
No, Sungjong ; Oh, Seung Sang ; Yoo, Hyungkee. / Bisected vertex leveling of plane graphs : Braid index, arc index and delta diagrams. In: Journal of Knot Theory and its Ramifications. 2018.
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