On upper bound graphs with forbidden subposets

For a poset P=(X,⩽P), the upper bound graph (UB-graph) of P is the graph UB(P)=(X,EUB(P)), where xy∈EUB(P) if and only if x≠y and there exists m∈X such that x,y⩽Pm. 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.