On minimal prime graphs and posets

Maurice Pouzet (1) , Imed Zaguia

1 ICJ - Institut Camille Jordan

We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.

Mots clés: Prime graph; prime poset; The neigborhood lattice of a graph; incidence structure; Galois lattice; Ramsey theorem

Domaines: Mathématique discrète [cs.DM]

Maurice Pouzet, Imed Zaguia. On minimal prime graphs and posets. Order, 2009, 26, pp.357-375. ⟨hal-00863170⟩