What are the conditions that an undirected bipartite graph $G=(U,V, E)$ should have to be colored as follows:
Nodes in $U$ are colored $-1$ or $+1$. The sign of a node $v \in V$ is the sum of the colors of the nodes in $U$ connected to $v$, i.e. $c(v) = \sum_{(v,u)\in E}{c(u)}$. A coloring is valid only if $0 \le c(v) \le 1, \forall{v \in V}$.
For example if $|V| = 2$, then we can always have a valid coloring.
Any help on this is greatly appreciated.