Chromatic polynomial, q-binomial counting and colored Jones function

Abstract

We define a q-chromatic function on graphs and compare it with existing graph functions. We also relate the q-chromatic function to the colored Jones function of knots.

This leads to a curious expression of the colored Jones function of a knot diagram as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams.

Keywords

• Chromatic
• polynomial
• q-binomial
• counting
• colored
• Jones
• function