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Spanning eulerian subgraphs, the splitting lemma, and Petersen’s theorem. (English) Zbl 0764.05051
A graph \(G=(V,E)\) is called eulerian graph if for each \(v\in V\), \(d(v)\) is even. Using the well-known theorem of Petersen: A bridgeless 3-regular graph has a spanning 2-regular subgraph, and the Splitting Lemma (Lemma III. 26 in H. Fleischner [Eulerian graphs and related topics, Part 1, Vol. 2, Ann. Discrete Math. 50 (1991)]), the author shows that a bridgeless graph with minimum degree at least 3 has a spanning eulerian subgraph without isolated vertices. The result can be viewed as a generalization of Petersen’s theorem.
Reviewer: F.Tian (Beijing)

MSC:
05C45 Eulerian and Hamiltonian graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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[1] Fleischner, H., Eularian graphs and related topics, part 1, ()
[2] Fleischner, H., Eularian graphs and related topics, part 1, ()
[3] Fleischner, H., On spanning subgraphs of a connected bridgeless graph and their application to DT-graphs, J. combin. theory ser. B, 1, 17-28, (1974) · Zbl 0256.05120
[4] Jaeger, F., Flows and generalized coloring theorems in graphs, J. combin. theory ser. B, 26, 205-216, (1979) · Zbl 0422.05028
[5] Kundu, S., Bounds on the number of disjoint spanning trees, J. combin. theory ser. B, 17, 199-203, (1974) · Zbl 0285.05113
[6] Polesski, V.P., A lower boundary for the reliability of information networks, 250th Anniversary Conference on Graph Theory (Fort Wayne, IN, 1986), Problems inform. transmission, 7, 165-171, (1971)
[7] Catlin, P.A., Supereulerian graphs, Congr. numer., 64, 59-72, (1988)
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