# Capacity-obeying packing

From Egres Open

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