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Even subgraphs of bridgeless graphs and 2-factors of line graphs. (English) Zbl 1127.05080
Summary: By Petersen’s theorem, a bridgeless cubic multigraph has a 2-factor. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph [see H. Fleischner, Discrete Math. 101, No. 1–3, 33–37 (1992; Zbl 0764.05051)]. Our main result is that every bridgeless simple graph with minimum degree at least three has a spanning even subgraph in which every component has at least four vertices. We deduce that if \(G\) is a simple bridgeless graph with \(n\) vertices and minimum degree at least three, then its line graph has a 2-factor with at most \(\max\{1,(3n-4)/10\}\) components. This upper bound is best possible.

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
Citations:
Zbl 0764.05051
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