Comparability graph: различия между версиями

'''Comparability graph''' — ''[[граф сравнимости]].''

Let <math>\,G = (V,E)</math> be an [[undirected graph]] and let <math>\,F</math> be an ''orientation'' of its [[edge|edges]] (i.e. <math>\,(V,F)</math> is the resulting [[oriented graph]]).

<math>\,F</math> is called a '''[[transitive orientation]]''' of <math>\,G</math> if the following

<math>\,F \cap F^{-1} = \emptyset\mbox{ and }F + F^{-1} = E\mbox{ and }F^{2} \subseteq F,</math>

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

A [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> which admits a '''transitive orientation''' of its edges is called a '''comparability graph'''.

If graph <math>\,G</math> is a '''comparability''' graph, then this also holds for every [[induced

subgraph]] of <math>\,G</math>.

The other name is a '''[[Transitively orientable graph]]'''.

 

 

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