Is the following decision problem NP-complete:
Let $G$ be an undirected graph and $b \le c$ two integers. Is it possible to select for every vertex of $G$ exactly $b$ different neighbors such that no node is chosen more then $c$ times.
The case $b = 1$ can be solved for any $c$ in polynomial time using maximal matching.
Motivation: Each node wants to place $b$ backups at different neighbors, but each node has only capacity to store $c$ backups.