SPANNING TRAILS AVOIDING AND CONTAINING GIVEN EDGES

Let ,kappa'(G) denote the edge connectivity of a graph G. For any disjoint subsets X, Y subset of E(G) with |Y | <= ,kappa'(G) - 1, a necessary and sufficient condition for G - Y to be a contractible configuration for G containing a spanning closed trail is obtained. We also characterize the structure of a graph G that has a spanning closed trail containing X and avoiding Y when |X| + |Y | <= ,kappa'(G). These results are applied to show that if G is (s, t) sup ereulerian (that is, for any disjoint subsets X, Y subset of E(G) with |X| <= s and |Y | <= t, G has a spanning closed trail that contains X and avoids Y ) with ,kappa'(G) = delta(G) >= 3, then for any permutation alpha on the vertex set V (G), the permutation graph alpha(G) is (s, t)-sup ereulerian if and only if s+t <= ,kappa'(G).