chromaticIdeal -- chromatic ideal of a graph

Synopsis

Usage:

chromaticIdeal(kk,G,q)
Inputs:
- kk, a ring
- G, an instance of the type Graph
- q, an integer
Outputs:
- an ideal

Description

Returns the ideal of proper q-colorings of a graph G=(V,E), given by the equations x_i^q -1, i ∈V and (x_i^q-x_j^q)/(x_i-x_j), ij∈E.

i1 : G = cycleGraph 4;

i2 : I = chromaticIdeal(QQ, G, 3)

             2          2   2          2   2          2   2          2   3       3       3       3
o2 = ideal (a  + a*b + b , a  + a*d + d , b  + b*c + c , c  + c*d + d , a  - 1, b  - 1, c  - 1, d  - 1)

o2 : Ideal of QQ[a, b, c, d]