A spanning tree expansion of the Jones polynomial
This paper presents a reformulation of the bracket polynomial of Kauffman (and hence of the Jones polynomial) for an oriented link, based on ideas related to the Tutte polynomial of graph theory. The bracket polynomial is expressed as a sum of monomials, indexed by the set of spanning trees of the graph associated with a black-and-white colouring of the regions of a link diagram. Some interesting connections between the crossing number of alternating link diagrams and the reduced degree (''breadth'') of the Jones polynomial (also observed in part by Kauffman and by Murasugi) follow from this approach.
crossing number of alternating link diagrams
scientific article; zbMATH DE number 4009330