Abstract:Let κ (G) denote the edge connectivity of a graph G. For any disjoint subsets X, Y ⊆ E(G) with |Y | ≤ κ (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 | ≤ κ (G). These results are applied to show that if G is (s, t)supereulerian (that is, for any disjoint subsets X, Y ⊆ E(G) with |X| ≤ s and |… Show more
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