Even subgraphs of bridgeless graphs and 2-factors of line graphs

By Petersen’s theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least 3 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 3, then its line graph has a 2-factor with at most max{1, (3n− 4)/10} components. This upper bound is best possible.