Abstract
We prove that a graphG admits a 2-factorF whenever there is an edgeuv such that bothG − u andG − v have a 2-factor; moreover we can takeF to be contained in the union of these 2-factors (and the edgeuv) and to contain their intersection. These results are generalized to certainf-factors and analogous results are obtained for bipartite and for directed graphs.
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Fraisse, P., Hell, P. & Kirkpatrick, D.G. A note onf-factors in directed and undirected multigraphs. Graphs and Combinatorics 2, 61–66 (1986). https://doi.org/10.1007/BF01788078
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DOI: https://doi.org/10.1007/BF01788078