Graham–Rothschild theorem
E748751
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Graham–Rothschild theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8657126 — 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: Graham–Rothschild theorem Context triple: [Ronald L. Graham, notableIdea, Graham–Rothschild theorem]
-
A.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
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B.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
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C.
Ramsey theory
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.
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D.
Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
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E.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
- 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: Graham–Rothschild theorem Target entity description: The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
-
A.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
-
B.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
-
C.
Ramsey theory
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.
-
D.
Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
-
E.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in Ramsey theory ⓘ |
| appliesTo |
combinatorial cubes
ⓘ
finite colorings ⓘ parameter sets ⓘ |
| characterizes | existence of large monochromatic structured subsets ⓘ |
| concerns |
colorings of combinatorial configurations
ⓘ
colorings of parameter words over finite alphabets ⓘ higher-dimensional combinatorial structures ⓘ parameter words ⓘ |
| field |
Ramsey theory
NERFINISHED
ⓘ
combinatorics ⓘ |
| frameworkFor | unifying various partition theorems ⓘ |
| generalizes |
Hales–Jewett theorem
NERFINISHED
ⓘ
classical partition theorems ⓘ van der Waerden’s theorem NERFINISHED ⓘ |
| guarantees | existence of monochromatic combinatorial substructures ⓘ |
| hasConcept |
parameter sets in combinatorics
ⓘ
structured monochromatic sets ⓘ |
| hasProperty |
finite version of an infinitary Ramsey principle
ⓘ
highly general framework for partition theorems ⓘ |
| implies |
Hales–Jewett theorem
NERFINISHED
ⓘ
van der Waerden’s theorem NERFINISHED ⓘ |
| introducedBy |
Bruce Rothschild
NERFINISHED
ⓘ
Ronald Graham NERFINISHED ⓘ |
| isPartOf | structural Ramsey theory NERFINISHED ⓘ |
| levelOfGenerality | higher-dimensional ⓘ |
| mathematicalDiscipline | discrete mathematics ⓘ |
| namedAfter |
Bruce Rothschild
NERFINISHED
ⓘ
Ronald Graham NERFINISHED ⓘ |
| relatedTo |
Gallai–Witt theorem
NERFINISHED
ⓘ
Hindman’s theorem NERFINISHED ⓘ Ramsey’s theorem NERFINISHED ⓘ |
| studiedIn |
Ramsey theory monographs
ⓘ
advanced combinatorics literature ⓘ |
| topic |
Ramsey-type phenomena
ⓘ
colorings of finite structures ⓘ combinatorial partitions ⓘ |
| type | partition theorem ⓘ |
| usedIn |
combinatorial number theory
ⓘ
higher-dimensional Ramsey theory NERFINISHED ⓘ theory of partition regularity ⓘ |
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: Graham–Rothschild theorem Description of subject: The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.