Abstract We show that determining the Jones polynomial of an alternating link is #P-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the… Expand

Let G be a 4-regular graph. For every vertex v of G, there are three distinct possible ways of splitting v into two vertices of degree two, which we call transitions at v. A transition system of G is… Expand

A type II matrix is a square matrixW with non-zero complex entries such that the entrywise quotient of any two distinct rows of W sums to zero. Hadamard matrices and character tables of abelian… Expand

We present an algebraic proof of the following result: a set of edges of a multigraph G is contained in some cycle of G iff the set contains no odd cocycle of G (“cycle” means here: edge disjoint sum… Expand

A balanced valuation of a multigraph H is a mapping w of its vertex-set V(H) into R such that VS C V(H) the number of edges of H with exactly one vertex in S is greater than or equal to IXvEsw(v)1;… Expand

We study spin models for invariants of links as defined by Jones [22]. We consider the two algebras generated by the weight matrices of such models under ordinary or Hadamard product and establish an… Expand