An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let ${\mathcal P}_{1}, \ldots, {\mathcal P}_{n}$ be additive hereditary graph properties. A graph $\,G$ has a property $({\mathcal P}_{1} \circ \cdots \circ {\mathcal P}_{n})$ if there is a partition $(V_{1}, \ldots, V_{n})$ of $\,V(G)$ into $,n$ sets such that, for all $\,i$, the induced subgraph $\,G[V_{i}]$ is in ${\mathcal P}_{i}$. A property ${\mathcal P}$ is reducible if there are properties ${\mathcal Q}$ , ${\mathcal R}$ such that ${\mathcal P} = {\mathcal Q} \circ {\mathcal R}$; otherwise it is irreducible.