Abstract
A finite order P on a set V is reconstructible (respectively, reconstructible up to duality) by its comparability graph if each order on V which has the same comparability graph as P is isomorphic to P (respectively, is isomorphic to P or to its dual P star). In this paper, we describe the finite orders which are reconstructible up to duality by their comparability graphs. This result is motivated by the characterization, obtained by Gallai (Acta Math Acad Sci Hungar 18:25-66, 1967), of the pairs of finite orders having the same comparability graph. Notice that a characterization of the finite orders which are reconstructible by their comparability graphs is easily deduced from Gallai's result.