# Comparability graph

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Comparability graphграф сравнимости.

Let $\,G = (V,E)$ be an undirected graph and let $\,F$ be an orientation of its edges (i.e. $\,(V,F)$ is the resulting oriented graph). $\,F$ is called a transitive orientation of $\,G$ if the following properties hold:

$\,F \cap F^{-1} = \emptyset\mbox{ and }F + F^{-1} = E\mbox{ and }F^{2} \subseteq F,$

where $\,F^{2} = \{(a,c)| \; \exists_{b \in V}(a,b) \in F \wedge (b,c) \in F\}$.

A graph $\,G$ which admits a transitive orientation of its edges is called a comparability graph.

If graph $\,G$ is a comparability graph, then this also holds for every [[induced subgraph]] of $\,G$.

The other name is a Transitively orientable graph.

## Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.