spanningTree -- returns a spanning tree of a graph

i1 : R = QQ[x_1..x_6];

i2 : C = cycle R; -- a 6-cycle

i3 : spanningTree C

o3 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                         1   2     3   4     4   5     1   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o3 : Graph

i4 : T = graph {x_1*x_2,x_2*x_3, x_1*x_4,x_1*x_5,x_5*x_6}; -- a tree (no cycles)

i5 : T == spanningTree T

o5 = true

i6 : G = graph {x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4}; -- two three cycles

i7 : spanningTree G

o7 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }}}
                         1   3     2   3     4   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o7 : Graph