Knots, spin models and graphs. (Knoten, Spin Modelle und Graphen.) (German) Zbl 0859.57004

Starting from the Reidemeister moves for knots and links the paper discusses the spin models introduced by Jones as well as the Yang-Baxter equations. It is then the main intention of the paper two show how this approach to the problem of distinguishing knots leads in a natural way to some of the most famous open problems of combinatorics and graph theory (existence of designs, orthogonal latin squares and projective planes, existence of Hadamard matrices), by interpreting and constructing spin models in terms of graph theoretical properties. In this context, also the Jones and Kauffman polynomials are discussed.


57M25 Knots and links in the \(3\)-sphere (MSC2010)
05C99 Graph theory