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

Sungjong No; Seung Sang Oh; Hyungkee Yoo

doi:10.1142/S021821651850044X

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

Sungjong No, Seung Sang Oh, Hyungkee Yoo

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 (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 language	English
Journal	Journal of Knot Theory and its Ramifications
DOIs	https://doi.org/10.1142/S021821651850044X
Publication status	Accepted/In press - 2018 Jun 8

Keywords

arc index
braid index
delta diagram
Knot
link

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1142/S021821651850044X

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AU - Yoo, Hyungkee

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KW - delta diagram

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KW - link

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