Reconstruction of Posets with the Same Comparability Graph

Given two finite posetsPandP′ with the same comparability graph, we show that if |V(P)|⩾4 and if for allx∈V(P),P−x≃P′−x, thenP≃P′. This result leads us to characterize the finite posetsPsuch that for allx∈V(P),P−x≃P*−x.