On double bound graphs and forbidden subposets

For a poset P = ( X , ⩽ P ) , the double bound graph (DB-graph) of P is the graph D B ( P ) = ( X , E D B ( P ) ) , where x y ∈ E D B ( P ) if and only if x ≠ y and there exists n , m ∈ X such that n ⩽ P x , y ⩽ P m . We show some characterizations on split double bound graphs, threshold double bound graphs and difference double bound graphs in terms of ( n , m ) -subposets and double canonical posets.