On upper bound graphs with forbidden subposets

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