-- -*- M2-comint -*- {* hash: -861223358 *}

i1 : S = QQ[a..e];

i2 : t = graph {a*b,b*c,c*d,a*e} -- a tree (and thus, bipartite)

o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o2 : Graph

i3 : c5 = cycle S -- 5-cycle (not bipartite)

o3 = Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}, {a, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o3 : Graph

i4 : isBipartite t

o4 = true

i5 : isBipartite c5

o5 = false

i6 :