A Note On Edge Connectivity and Parity Factor

Abstract

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

5 pages