Minimal reducible bounds for the class of k-degenerate graphs

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Abstract

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

MSC

05C15
O5C75

Keywords

k-degenerate graph
Property of graphs
Additive
Hereditary
Vertex partition
Minimal reducible bounds

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