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 | |
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