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In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial. ==Rules of tricolorability== A knot is tricolorable if each strand of the knot diagram can be colored one of three colors, subject to the following rules:〔Weisstein, Eric W. (2010). ''CRC Concise Encyclopedia of Mathematics'', Second Edition, p.3045. ISBN 9781420035223. quoted at Accessed: May 5, 2013.〕 :1. At least two colors must be used, and :2. At each crossing, the three incident strands are either all the same color or all different colors. Some references state instead that all three colors must be used.〔Gilbert, N.D. and Porter, T. (1994) ''Knots and Surfaces'', p. 8〕 For a knot, this is equivalent to the definition above; however, for a link it is not. "The trefoil knot and trivial 2-link are tricolorable, but the unknot, Whitehead link, and figure-eight knot are not. If the projection of a knot is tricolorable, then Reidemeister moves on the knot preserve tricolorability, so either every projection of a knot is tricolorable or none is."〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tricolorability」の詳細全文を読む スポンサード リンク
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