Looking for some hint on a question in an assignment
"Find a graph which has some vertices u, v and w such that there is a cycle containing both u and v, a cycle containing both v and w, but no cycle containing both u and w."
I don't get how that is even possible. a cycle containing both u and v, means there are path: u -> v path: v -> u.
a cycle for v and w, means there is path: v -> w path: w -> v
then shouldnt that imply there is a cycle containing u and w. because to get from u to w, we take path u->v, then v->w to get from w to u, we take path w->v, then v->u
I dont get how this question is possible