chromaticIdeal -- chromatic ideal of a graph

Synopsis

Usage:

chromaticIdeal(kk,G,q)
Inputs:
- kk, a ring,
- G, a 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 $x_i^q -1, i \in V$ and $(x_i^q-x_j^q)/(x_i-x_j), ij\in E$.

i1 : G = cycleGraph 4;

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

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

o2 : Ideal of QQ[a..d]

For the programmer

The object chromaticIdeal is a function closure.