Graham–Rothschild theorem

E748751

mathematical theorem result in Ramsey theory

The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.

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Label	Occurrences
Graham–Rothschild theorem canonical	1

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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.
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
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 ⓘ combinatorics ⓘ
frameworkFor	unifying various partition theorems ⓘ
generalizes	Hales–Jewett theorem ⓘ classical partition theorems ⓘ van der Waerden’s theorem ⓘ linked to: van der Waerden theorem
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 ⓘ van der Waerden’s theorem ⓘ linked to: van der Waerden theorem
introducedBy	Bruce Rothschild ⓘ linked to: Bruce L. Rothschild Ronald Graham ⓘ linked to: Ronald L. Graham
isPartOf	structural Ramsey theory ⓘ linked to: Ramsey theory
levelOfGenerality	higher-dimensional ⓘ
mathematicalDiscipline	discrete mathematics ⓘ
namedAfter	Bruce Rothschild ⓘ linked to: Bruce L. Rothschild Ronald Graham ⓘ linked to: Ronald L. Graham
relatedTo	Gallai–Witt theorem ⓘ Hindman’s theorem ⓘ linked to: Hindman theorem Ramsey’s theorem ⓘ linked to: Ramsey theory
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 ⓘ linked to: Ramsey theory theory of partition regularity ⓘ

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Ronald L. Graham → notableIdea → Graham–Rothschild theorem ⓘ

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Statements (42)

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