Spanning eulerian subgraphs, the splitting lemma, and Petersen’s theorem.

*(English)*Zbl 0764.05051A 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.) |

##### Keywords:

splitting lemma; eulerian graph; bridgeless graph; spanning eulerian subgraph; Petersen’s theorem
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\textit{H. Fleischner}, Discrete Math. 101, No. 1--3, 33--37 (1992; Zbl 0764.05051)

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##### References:

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