On edge connectivity and parity factor

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 m e > 0 be even and m o > 0 be odd. In this paper, we prove that every m e -edge-connected graph with minimum degree at least m e + 1 contains an even factor with minimum degree at least m e and every (m o + 1)-edge-connected graph contains an odd factor with minimum degree at least m o , which further extends Fleischner.s result. Moreover, we show that our results are best possible.