Abstract
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition.
D. Stanovský—Partially supported by the GAČR grant 13-01832S.
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Fish, A., Lisitsa, A., Stanovský, D. (2015). A Combinatorial Approach to Knot Recognition. In: Horne, R. (eds) Embracing Global Computing in Emerging Economies. EGC 2015. Communications in Computer and Information Science, vol 514. Springer, Cham. https://doi.org/10.1007/978-3-319-25043-4_7
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