Tricolorability is a property of a knot that indicates whether it can be colored using three colors in such a way that no two adjacent segments (crossings) share the same color. This concept helps identify whether a knot is nontrivial or can be simplified, providing insight into the knot's structure and equivalence with other knots. Tricolorability connects to knot invariants, as it serves as one way to distinguish between different knots and their properties, particularly when classifying knots based on crossing numbers.
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