The incompatibility of crossing number and bridge number for knot diagrams
نویسندگان
چکیده
منابع مشابه
The Crossing Number and Maximal Bridge Length of a Knot Diagram
We give examples showing that Kidwell’s inequality for the maximal degree of the Brandt-LickorishMillett-Ho polynomial is in general not sharp.
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The crossing number crðGÞ of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcrðGÞ is the smallest number of pairs of edges that cross in a drawing of G in the plane. While crðGÞXpcrðGÞ holds trivially, it is not known whether a strict inequality can ever occur (this question was raised by Mohar and Pach and Tóth). We ai...
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A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of ∂M . We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found b...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.03.013