  Let $G=(X,Y;E)$ be a bipartite graph, where $X$ and $Y$ are color classes and
$E$ is the set of edges of $G$. Lov\'asz and Plummer \cite{LoPl86} asked
whether one can decide in polynomial time that a given bipartite graph $G=(X,Y;
E)$ admits a 1-anti-factor, that is subset $F$ of $E$ such that $d_F(v)=1$ for
all $v\in X$ and $d_F(v)\neq 1$ for all $v\in Y$. Cornu\'ejols \cite{CHP}
answered this question in the affirmative. Yu and Liu \cite{YL09} asked
whether, for a given integer $k\geq 3$, every $k$-regular bipartite graph
contains a 1-anti-factor. This paper answers this question in the affirmative.
