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Spanning even subgraphs of 3-edge-connected graphs. (English) Zbl 1180.05057
Summary: By Petersen’s theorem, a bridgeless cubic graph has a 2-factor. H. Fleischner [“Spanning eulerian subgraphs, the splitting lemma, and Petersen’s theorem”, Discrete Math. 101, No.1-3, 33–37 (1992: Zbl 0764.05051)] extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3-edge-connectivity, we can find a spanning even subgraph in which every component has at least five vertices. We show that this is in some sense best possible by constructing an infinite family of 3-edge-connected graphs in which every spanning even subgraph has a 5-cycle as a component.

MSC:
05C38 Paths and cycles
05C40 Connectivity
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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