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Chordal :: chromaticIdeal

chromaticIdeal -- chromatic ideal of a graph

Synopsis

Description

Returns the ideal of proper q-colorings of a graph G=(V,E), given by the equations xiq -1, i ∈V and (xiq-xjq)/(xi-xj), ij∈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, b, c, d]