Abstract
By Petersen’s Theorem, a bridgeless cubic graph has a 2-factor. Fleischner (Discrete Math., 101, 33–37 (1992)) has extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has an even factor without isolated vertices. Let me > 0 be even and mo > 0 be odd. In this paper, we prove that every me-edge-connected graph with minimum degree at least me + 1 contains an even factor with minimum degree at least me and every (mo + 1)-edge-connected graph contains an odd factor with minimum degree at least mo, which further extends Fleischner’s result. Moreover, we show that our results are best possible.
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