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

作者：No Sungjong; Oh Seungsang^*; Yoo Hyungkee

来源：Journal of Knot Theory and Its Ramifications, 2018, 27(8): 1850044.

DOI：10.1142/S021821651850044X

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

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 alpha(L) for any knot or non-split link L, which are b(L) <= 1/2c(L) + 1 and alpha(L) <= c(L) + 2. We also find a quadratic upper bound of the minimal crossing number of delta diagrams of L.

• 出版日期2018-7