Link polynomials derived from magnetic graphs

Link Discovery in Graphs Derived from Biological Databases

Public biological databases contain vast amounts of rich data that can also be used to create and evaluate new biological hypothesis. We propose a method for link discovery in biological databases, i.e., for prediction and evaluation of implicit or previously unknown connections between biological entities and concepts. In our framework, information extracted from available databases is represe...

Tutte Polynomials of Flower Graphs

Graph polynomials derived from Tutte-Martin polynomials

A graph polynomial q(G; ) has recently been studied byArratia et al. [The interlace polynomial: a new graph polynomial, in: Proceedings of the EleventhAnnual ACM-SIAM Symposium on Discrete Mathematics, San Francisco, CA, 2000, North-Holland, Amsterdam, pp. 237–245]. That polynomial can be derived from the restricted Tutte–Martin polynomial of an isotropic system, which we introduced [A. Bouchet...

A Dichromatic Polynomial for Weighted Graphs and Link Polynomials

A dichromatic polynomial for weighted graphs is presented. The Kauffman bracket of a signed graph, an invariant inspired by the Jones polynomial of a link in three-space, is shown to be essentially an evaluation of this dichromatic polynomial, as are the homfly polynomials of certain particular types of links. 1. THE DICHROMATIC POLYNOMIAL OF A WEIGHTED GRAPH In this note we use the term graph ...

Tutte Polynomials and Link Polynomials

We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.