A spectral radius condition for a graph to have $(a,b)$-parity factors

Abstract

Let $a,b$ be two positive integers such that $a\le b$ and $a\equiv b$ (mod $2$). We say that a graph $G$ has an $(a,b)$-parity factor if $G$ has a spanning subgraph $F$ such that $d_F(v)\equiv b$ (mod $2$) and $a\le d_F(v)\le b$ for all $v\in V(G)$. In this paper, we provide a tight spectral radius condition for a graph to have $(a,b)$-parity factors.

12 pages