Journal article
Neighbors of Knots in the Gordian Graph
The American mathematical monthly, Vol.124(1), pp.4-23
01/01/2017
DOI: 10.4169/amer.math.monthly.124.1.4
Abstract
The Gordian graph is the graph with vertex set the set of knot types and edge set consisting of pairs of knots that have a diagram wherein they differ at a single crossing. The bridge number is a classical knot invariant that is a measure of the complexity of a knot. It can be refined by another, recently discovered, knot invariant known as "bridge distance." We show, using arguments that are almost entirely elementary, that each vertex of the Gordian graph is adjacent to a vertex having arbitrarily high bridge number and bridge distance.
Details
- Title: Subtitle
- Neighbors of Knots in the Gordian Graph
- Creators
- Ryan Blair - Calif State Univ Long Beach, Long Beach, CA 90840 USAMarion Campisi - San Jose State UniversityJesse Johnson - Oklahoma State UniversityScott A Taylor - Colby Coll, Waterville, ME 04901 USAMaggy Tomova - Univ Iowa, Iowa City, IA 52240 USA
- Resource Type
- Journal article
- Publication Details
- The American mathematical monthly, Vol.124(1), pp.4-23
- DOI
- 10.4169/amer.math.monthly.124.1.4
- ISSN
- 0002-9890
- eISSN
- 1930-0972
- Publisher
- MATHEMATICAL ASSOC AMER
- Number of pages
- 20
- Grant note
- American Institute of Mathematics for its support through the SQuaREs program Colby College Division of Natural Sciences DMS-1006369; DMS-1054450 / NSF Grant
- Language
- English
- Date published
- 01/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984241038002771
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