Spanning eulerian subgraphs, the splitting lemma, and Petersen's theorem (Q1197011)

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 \textit{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.