Graphes et ordonnés démontables, propriété de la clique fixe

This work extends to dismantable graphs many properties of dismantable posets dealing with products, exponentiation, existence of paths in a graph of all homomorphisms, fixed clique property, etc. We show that a poset is dismantlable in the sense of Rival if and only if its comparability graph is dismantlable, thus proving that, for posets, dismantlability is a comparability invariant. We establish the analogues for graphs of results of Duffus, Poguntke and Rival about fixed point sets and cores in posets.