On the Choosability of Bipartite Graphs

Abstract

Let $u$ be an odd vertex of a bipartite graph $B$ and suppose that $f:V(B)\to \mathbb{N}$ is a function such that $f(u)=\lceil d_B(u)/2\rceil$ and $f(v)=\lceil d_B(v)/2\rceil +1$ for $v\in V(B)\setminus u$, where $d_B(v)$ is the degree of $v$ in $B$. In this paper, we prove that $B$ is $f$-choosable.