We investigate properties of reducible J-holomorphic subvarieties in 4-manifolds. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is J-nef.

For a spherical class, it has particularly strong consequences: for any tamed J, each irreducible component is a smooth rational curve. We also completely classify configurations of maximal dimension. To prove these results we treat subvarieties as weighted graphs and introduce several combinatorial moves. This is a joint work with Weiyi Zhang.