BEST theorem
E824089
The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
All labels observed (1)
| Label | Occurrences |
|---|---|
| BEST theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9838897 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: BEST theorem Context triple: [de Bruijn–van Aardenne–Ehrenfest theorem, relatedTo, BEST theorem]
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A.
Teorema
Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
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B.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
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C.
Best
Best is a common English surname borne by numerous notable individuals across sports, arts, and public life.
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D.
Best
Best is a town and municipality in the southern Netherlands, located in the province of North Brabant near the city of Eindhoven.
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E.
Thales’ theorem
Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: BEST theorem Target entity description: The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
-
A.
Teorema
Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
-
B.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
C.
Best
Best is a common English surname borne by numerous notable individuals across sports, arts, and public life.
-
D.
Best
Best is a town and municipality in the southern Netherlands, located in the province of North Brabant near the city of Eindhoven.
-
E.
Thales’ theorem
Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
result in graph theory
ⓘ
theorem ⓘ |
| appliesTo |
Eulerian directed graph
ⓘ
directed graph ⓘ |
| area | enumerative combinatorics ⓘ |
| assumes |
in-degree equals out-degree at every vertex
ⓘ
strongly connected directed graph ⓘ |
| category | theorem in discrete mathematics ⓘ |
| concerns |
Eulerian circuit
ⓘ
counting Eulerian circuits ⓘ |
| doesNotApplyTo | non-Eulerian directed graphs ⓘ |
| field | graph theory ⓘ |
| formulaInvolves |
number of spanning in-arborescences rooted at a vertex
ⓘ
product of factorials of out-degrees minus one ⓘ |
| generalizes | counting formula for Eulerian circuits in undirected graphs via orientations ⓘ |
| givesCountAs | T_r × ∏_v (outdeg(v) − 1)! for a root r ⓘ |
| givesFormulaFor | number of distinct Eulerian circuits in a directed graph ⓘ |
| hasKeyCondition |
graph must be Eulerian
ⓘ
graph must be strongly connected ⓘ |
| holdsFor | finite directed graphs ⓘ |
| implies | existence of at least one Eulerian circuit in an Eulerian digraph ⓘ |
| nameAcronymOf | de Bruijn–van Aardenne-Ehrenfest–Smith–Tutte theorem NERFINISHED ⓘ |
| namedAfter |
Smith
NERFINISHED
ⓘ
Tutte NERFINISHED ⓘ de Bruijn NERFINISHED ⓘ van Aardenne-Ehrenfest NERFINISHED ⓘ |
| originallyProvedBy |
Cedric A. B. Smith
NERFINISHED
ⓘ
Nicolaas Govert de Bruijn NERFINISHED ⓘ Tatyana van Aardenne-Ehrenfest NERFINISHED ⓘ William T. Tutte NERFINISHED ⓘ |
| relatedTo |
Eulerian trail
NERFINISHED
ⓘ
Matrix-Tree theorem NERFINISHED ⓘ de Bruijn graph NERFINISHED ⓘ |
| relates | Eulerian circuits and spanning arborescences ⓘ |
| requires | choice of a root vertex ⓘ |
| usedFor |
analysis of network routing structures
ⓘ
combinatorial enumeration problems ⓘ counting Eulerian cycles in de Bruijn graphs ⓘ |
| usedIn |
coding theory
ⓘ
design of de Bruijn sequences ⓘ theoretical computer science ⓘ |
| usesConcept |
spanning arborescence
ⓘ
vertex in-degree ⓘ vertex out-degree ⓘ |
| usesTool | Matrix-Tree theorem NERFINISHED ⓘ |
| yearIntroducedApprox | 1950s ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: BEST theorem Description of subject: The BEST theorem is a result in graph theory that gives a formula for counting the number of distinct Eulerian circuits in a directed graph using spanning arborescences and vertex degrees.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.