Comparability graph
![Hasse diagram of a poset (left) and its comparability graph (right)](/Images/godic/202501/05/Poset_et_graphe_de_comparabilité.svg1013.png")
![One of the forbidden induced subgraphs of a comparability graph. The generalized cycle
a–b–d–f–d–c–e–c–b–a in this graph has odd length (nine) but has no triangular chords.](/Images/godic/202501/05/Forbidden_interval_subgraph.svg1013.png")
In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, and containment graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order.