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In this paper, we investigate some parity factors by using Lov\'asz's(g,f)-parity theorem. Let $m>0$ be an integer. Firstly, we obtain a sufficientand necessary condition for some graphs to have a parity factor with restrictedminimum degree. Secondly, we obtain some sufficient conditions for a graph tohave a parity factor with minimum degree $m$ in term of edge connectivity.

A Note On Edge Connectivity and Parity Factor