Coloring Graphs from Knots

Title: Coloring Graphs from Knots
Author: Brandon Amerine
Date: 27 May 2021
Type: Text; Image; MovingImage; StillImage
Identifier: aes/277
Language: eng
Abstract: Knots and links can be categorized by invariants such as colorability. A knot is a three-dimensional object, so any two-dimensional diagram of that knot must consist of a set of crossings and set of strands that indicate the behavior of the three-dimensional object. Past authors have defined knot coloring using a system of equations at the crossings in the knot diagram. Since we can associate a knot with a strand adjacency graph, here we investigate whether a knot’s associated graph can be used to provide a non-algebraic version of colorability. We explore a couple different arrangements for a strand adjacency graph and the results that occur under several types of colorability. Along the way, we also take a look at cablings of knots and their distinctions from prime knots in these results.
Rights: Western Oregon University Library has determined, as of 05/27/2021, this item is in copyright, which is held by the author. Users may use the item in accordance with copyright limitations and exceptions, including fair use. For other uses, please ask permission from the author.; http://rightsstatements.org/vocab/InC/1.0/
Department: Mathematics
Faculty Sponsor: Ben Cote