Factorizations of properties of graphs
A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-partition of a graph G is a partition V₁,V₂,...,Vₙ of V(G) such that for each i = 1,2,...,n the induced subgraph has property . The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ;...