# Capacity-obeying packing

Let G=(V,E) be an undirected or directed graph, and $c:E \to {\mathbb Z}_+$ a capacity function on the edges. A capacity-obeying packing of subgraphs is a collection $G_1, \ldots, G_t$ of subgraphs of G with the property that each edge $e\in E$ is contained in at most c(e) of these subgraphs. An analogous definition can be given for hypergraphs.