Minimal reducible bounds for the class of [formula omitted]-degenerate graphs

Abstract

Let ( L a,⊆) be the lattice of hereditary and additive properties of graphs. A reducible property R∈ L a is called minimal reducible bound for a property P∈ L a if in the interval ( P, R) of the lattice L a , there are only irreducible properties. We prove that the set B( D k)={ D p∘ D q : k=p+q+1} is the covering set of minimal reducible bounds for the class D k of all k-degenerate graphs.