Maximal packing

Maximal packing --- максимальная упаковка.

A maximal packing of a digraph [math]\displaystyle{ D = (V, A) }[/math] with isomorphic copies of a digraph [math]\displaystyle{ d }[/math] is a set [math]\displaystyle{ \{d_{1}, d_{2}, \ldots, d_{n}\} }[/math], where [math]\displaystyle{ d_{i} \cong d }[/math] and [math]\displaystyle{ V(d_{i}) \subset V(D) }[/math] for all [math]\displaystyle{ i }[/math], [math]\displaystyle{ A(d_{i}) \cap A(d_{j}) = \emptyset }[/math] if [math]\displaystyle{ i \neq j }[/math], [math]\displaystyle{ \cup _{i=1}^{n} d_{i} \subset D }[/math] and

[math]\displaystyle{ \left|A(D) \setminus \cup_{i=1}^{n} A(d_{i})\right | }[/math]

is minimal.

A maximal packing of [math]\displaystyle{ D }[/math] with isomorphic copies of [math]\displaystyle{ d }[/math] such that [math]\displaystyle{ \cup_{i=1}^{n} d_{i} = D }[/math] is an isomorphic decomposition of [math]\displaystyle{ D }[/math] into copies of [math]\displaystyle{ d }[/math] (or a [math]\displaystyle{ d }[/math]-decomposition of [math]\displaystyle{ D }[/math] for short).

Packings and decompositions of undirected graphs are similarly defined.