G-Trade

[math]\displaystyle{ G }[/math]-Trade --- [math]\displaystyle{ G }[/math]-трейд.

Given a simple graph [math]\displaystyle{ G }[/math], let [math]\displaystyle{ T_{1} }[/math] and [math]\displaystyle{ T_{2} }[/math] be two different decompositions of some graph [math]\displaystyle{ H }[/math] on [math]\displaystyle{ v }[/math] vertices into [math]\displaystyle{ s }[/math] edge-disjoint copies of [math]\displaystyle{ G }[/math], with the property that the copies of [math]\displaystyle{ G }[/math] in [math]\displaystyle{ T_{1} }[/math] are distinct from the copies of [math]\displaystyle{ G }[/math] in [math]\displaystyle{ T_{2} }[/math], that is, [math]\displaystyle{ T_{1} \cap T_{2} = \emptyset }[/math]. Then the pair [math]\displaystyle{ \{T_{1}, T_{2}\} }[/math] is a [math]\displaystyle{ G }[/math]-trade of volume [math]\displaystyle{ s }[/math] and foundation [math]\displaystyle{ v }[/math] denoted by [math]\displaystyle{ T_{G}(s;v) }[/math].

The copies of [math]\displaystyle{ G }[/math] in [math]\displaystyle{ T_{1} }[/math] and [math]\displaystyle{ T_{2} }[/math] are referred to as blocks. The trade is a Steiner trade provided that [math]\displaystyle{ H }[/math] is simple.

Such a [math]\displaystyle{ G }[/math]-trade is called a graphical trade to distinguish it from trades based on other combinatorial objects, such as blocks design and latin squares.