Ramsey theory
E381617
Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
All labels observed (10)
| Label | Occurrences |
|---|---|
| Ramsey theory canonical | 9 |
| Ramsey Theory (book) | 1 |
| Ramsey theorem | 1 |
| Ramsey theory in combinatorics | 1 |
| Ramsey's theorem | 1 |
| Ramsey-type theorem | 1 |
| Ramsey-type theorems | 1 |
| Ramsey’s theorem | 1 |
| structural Ramsey theory | 1 |
| van der Waerden theorem in combinatorics | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3725147 — 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: Ramsey theory Context triple: [F. P. Ramsey, notableWork, Ramsey theory]
-
A.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
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B.
Ulam problem in set theory
The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
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C.
Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
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D.
Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
-
E.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
- 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: Ramsey theory Target entity description: Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
-
A.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
-
B.
Ulam problem in set theory
The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
-
C.
Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
-
D.
Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
-
E.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
branch of combinatorics
ⓘ
branch of mathematics ⓘ |
| appliesTo |
finite sets
ⓘ
graphs ⓘ hypergraphs ⓘ infinite sets ⓘ integers ⓘ metric spaces ⓘ topological spaces ⓘ |
| basedOn |
infinite combinatorics
ⓘ
Dirichlet principle ⓘ
surface form:
pigeonhole principle
|
| fieldOfStudy | combinatorics ⓘ |
| hasCentralConcept |
Erdős–Rado theorem
ⓘ
Gallai theorem ⓘ Hales–Jewett theorem ⓘ Hindman theorem ⓘ Ramsey multiplicity ⓘ Ramsey number ⓘ Ramsey theory self-linksurface differs ⓘ
surface form:
Ramsey theorem
partition calculus ⓘ van der Waerden theorem ⓘ |
| hasProperty |
contains both finite and infinite versions of theorems
ⓘ
many problems are difficult or open ⓘ often yields very large bounds ⓘ |
| hasSubfield |
arithmetic Ramsey theory
ⓘ
graph Ramsey theory ⓘ hypergraph Ramsey theory ⓘ Ramsey theory self-linksurface differs ⓘ
surface form:
structural Ramsey theory
topological Ramsey theory ⓘ |
| historicalOrigin | early 20th century ⓘ |
| influencedBy |
On a Problem of Formal Logic
ⓘ
surface form:
Frank P. Ramsey 1930 paper on logic and combinatorics
|
| namedAfter |
F. P. Ramsey
ⓘ
surface form:
Frank P. Ramsey
|
| relatedTo |
additive combinatorics
ⓘ
computational complexity theory ⓘ extremal combinatorics ⓘ graph theory ⓘ logic ⓘ set theory ⓘ theoretical computer science ⓘ |
| studies |
Ramsey-type existence theorems
ⓘ
colorings of graphs and sets ⓘ conditions guaranteeing order in large structures ⓘ partition regularity ⓘ structural properties of large graphs ⓘ unavoidable patterns in sufficiently large objects ⓘ |
| usedIn |
ergodic theory
ⓘ
lower bounds in computational complexity ⓘ model theory ⓘ proofs of existence without explicit construction ⓘ |
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: Ramsey theory Description of subject: Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
Referenced by (18)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Ramsey's theorem
subject surface form:
Bartel Leendert van der Waerden
this entity surface form:
van der Waerden theorem in combinatorics
this entity surface form:
Ramsey Theory (book)
subject surface form:
Frank P. Ramsey
this entity surface form:
Ramsey theorem
this entity surface form:
structural Ramsey theory
this entity surface form:
Ramsey-type theorems
this entity surface form:
Ramsey’s theorem
this entity surface form:
Ramsey-type theorem
this entity surface form:
Ramsey theory in combinatorics