Graph coloring and the Jones polynomial

William Ballinger, Princeton University
Fine Hall 110

By interpreting a planar graph as giving an element in the Kauffman skein algebra, a polynomial invariant of graphs can be defined that turns out to be a reparametrization of the chromatic polynomial. This interpretation makes it clearer why the values of the chromatic polynomial at Beraha numbers should be of particular importance and leads to a family of generalizations of identities due originally to Tutte.