Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams
2018 ◽
Vol 27
(08)
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pp. 1850044
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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: see text] and arc index [Formula: see text] for any knot or non-split link [Formula: see text], which are [Formula: see text] and [Formula: see text]. We also find a quadratic upper bound of the minimal crossing number of delta diagrams of [Formula: see text].
2017 ◽
Vol 26
(14)
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pp. 1750100
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2019 ◽
Vol 28
(14)
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pp. 1950085
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2013 ◽
Vol 22
(6)
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pp. 935-954
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2011 ◽
Vol 20
(05)
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pp. 741-747
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2014 ◽
Vol 23
(07)
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pp. 1460008
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2010 ◽
Vol 19
(12)
◽
pp. 1655-1672
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