@article{5d0ad00db6e349749a658bcc6d1d85ee,
title = "Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams",
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.",
keywords = "Knot, arc index, braid index, delta diagram, link",
author = "Sungjong No and Seungsang Oh and Hyungkee Yoo",
note = "Funding Information: The author (Seungsang Oh) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. NRF-2017R1A2B2007216). Funding Information: The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",
year = "2018",
month = jul,
day = "1",
doi = "10.1142/S021821651850044X",
language = "English",
volume = "27",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "8",
}