-- -*- M2-comint -*- {* hash: 1875841829 *}

i1 : R = QQ[a,b,c,x,y,z];

i2 : completeMultiPartite(R,2,3)

o2 = Graph{edges => {{a, x}, {a, y}, {a, z}, {b, x}, {b, y}, {b, z}, {c, x}, {c, y}, {c, z}}}
           ring => R
           vertices => {a, b, c, x, y, z}

o2 : Graph

i3 : completeMultiPartite(R,{2,4})

o3 = Graph{edges => {{a, c}, {a, x}, {a, y}, {a, z}, {b, c}, {b, x}, {b, y}, {b, z}}}
           ring => R
           vertices => {a, b, c, x, y, z}

o3 : Graph

i4 : completeMultiPartite(R,{{a,b,c,x},{y,z}})

o4 = Graph{edges => {{a, y}, {a, z}, {b, y}, {b, z}, {c, y}, {c, z}, {x, y}, {x, z}}}
           ring => R
           vertices => {a, b, c, x, y, z}

o4 : Graph

i5 : R = QQ[a,b,c,d,e];

i6 : t1 = completeMultiPartite(R,5,1)

o6 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}}
           ring => R
           vertices => {a, b, c, d, e}

o6 : Graph

i7 : t2 = completeGraph R

o7 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}}
           ring => R
           vertices => {a, b, c, d, e}

o7 : Graph

i8 : t1 == t2

o8 = true

i9 :