Remarks on strong parity factors in graphs

Abstract

A graph $G$ has a strong parity factor $F$ if for any subset $X\subseteq V(G)$ with $|X|$ even, $G$ contains a spanning subgraph $F$ satisfying $\delta(F)\geq1$, $d_F(u)\equiv1$ (mod 2) for any $u\in X$, and $d_F(v)\equiv0$ (mod 2) for any $v\in V(G)\setminus X$. In this paper, we first establish a neighborhood condition for the existence of a strong parity factor in a graph. Then we show an independence number and minimum degree condition to ensure that a graph has a strong parity factor.