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

2018/06/25 by No, Sungjong, Oh, Seungsang, Yoo, Hyungkee · 1 citation
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1806.09719

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)/(2) c(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.

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• Weak rectangular diagrams, multi-crossing number, and arc index

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