A spectral condition for a graph to have strong parity factors

Abstract

A graph $G$ has the strong parity property if for every subset $X\subseteq V\left(G\right)$ with $\left|X\right|$ even, $G$ has a spanning subgraph $F$ satisfying $\delta \left(F\right)\ge 1$, $d_F\left(u\right)\equiv 1$ (mod 2) for any $u\in X$, and $d_F\left(v\right)\equiv 0$ (mod 2) for any $v\in V\left(G\right)\setminus X$. In this paper, we give a spectral radius condition to guarantee that a connected graph has the strong parity property.