Courcelle's theorem, in the study of graph algorithms, states that every graph property that can be defined in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth. The result was first proved by Bruno Courcelle in 1990 and was independently rediscovered by Borie, Parker and Tovey in 1992. It is regarded as the archetype of what are called algorithmic meta-theorems, results that convert logical expressiveness directly into an efficient algorithm.
Facts
Statementevery graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Courcelle's theorem - Wikipedia
Sources
1. Courcelle's theorem - Wikipedia
Lead section, first sentence
every graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth.
Lead section, second sentence
The result was first proved by Bruno Courcelle in 1990 and independently rediscovered by Borie, Parker & Tovey (1992).
In Branch: Logic and Foundations, Lead sentence
ph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth.
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