Tricolorable knots and links

simplest non-trivial closed knot with three crossings

thumb|right|A tricolored trefoil knot.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.

connected sum of two trefoil knots with opposite chirality

In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane.

mathematical knot with crossing number 6

connected sum of two trefoil knots with same chirality

mathematical knot with crossing number 7