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.
Amerine, Brandon, "Coloring Graphs from Knots" (2021). Academic Excellence Showcase Proceedings. 277.
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