Lattices, whose incomparability graphs have horns
In this paper, we study some graphs which are realizable and some which are not realizable as the incomparability graph (denoted by ??(L) ? ? ( L ) ) of a lattice L  with at least two atoms. We prove that the complete graph Kn K n with two horns is realizable as ??(L) ? ? ( L ) . We show that the complete graph K3 K 3 with three horns is not realizable as ??(L) ? ? ( L ) , however it is realizable as the zero-divisor graph of L . Also we give a necessary and sufficient condition for a complete bipartite graph with one horn and with two horns to be realizable as ??(L) ? ? ( L ) for some lattice L.
incomparability graph horn zero-divisor graph bipartite graph width of a lattice double star graph cozero-divisor graph