Spanning Eulerian subgraphs and matchings
Discrete Mathematics
Supereulerian graphs: a survey
Journal of Graph Theory
On dominating and spanning circuits in graphs
Proceedings of the first Malta conference on Graphs and combinatorics
Eulerian subgraphs containing given vertices and hamiltonian line graphs
Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
On factors of 4-connected claw-free graphs
Journal of Graph Theory
Eulerian subgraphs and Hamilton-connected line graphs
Discrete Applied Mathematics
Supereulerianity of k-edge-connected graphs with a restriction on small bonds
Discrete Applied Mathematics
Supereulerian graphs in the graph family C2(6,k)
Discrete Applied Mathematics
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A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut S ⊆ E(G) with |S| ≤ 3 satisfies the property that each component of G - S has order at least (n - 2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ ≥ 4: If G is a 2-edge-connected graph of order n with δ(G) ≥ 4 such that for every edge xy ∈ E(G) , we have max{d(x),d(y)} ≥ (n - 2)/5 - 1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G) ≥ 4 cannot be relaxed.