KnowraRamsey theoryLinked fromLinked fromThe 19 pages that link to Ramsey theory, each with the reason it gives.All 19Broader topic 2Related 6Narrower topic 11Paul ErdősRelated: Erdős developed foundational results about unavoidable patterns in large combinatorial systems.Probabilistic methodRelated: Random graphs give lower bounds on how large Ramsey numbers must be.Schur's theoremNarrower topic: Schur's theorem is an early finite-coloring result in additive Ramsey theory.Extremal combinatoricsRelated: Its guarantees often identify unavoidable substructures in large colored or dense objects.Ramsey's theoremNarrower topic: The theorem gives the field its central principle of finding order in arbitrary colorings.Frank P. RamseyBroader topic: His theorem on arithmetic progressions helped establish a mathematical field bearing his name.Richard RadoNarrower topic: Rado’s theorems helped establish the field’s central questions about unavoidable structure.Paris–Harrington theoremNarrower topic: The theorem is a finitary result in this broader area.Turán's theoremRelated: Turán bounds help quantify how many edges can remain without a prescribed clique.Erdős–Stone theoremRelated: Extremal bounds from the theorem can feed into arguments that force monochromatic graph structure.Hales–Jewett theoremNarrower topic: The theorem exemplifies the principle that disorder forces a monochromatic pattern.Erdős–Rado theoremNarrower topic: The theorem provides an infinite-cardinal guarantee within Ramsey theory.Lovász local lemmaRelated: The lemma helps construct colorings that avoid specified monochromatic substructures.History of combinatoricsBroader topic: Its results reveal a characteristic modern theme: unavoidable patterns within disorder.Big-line-big-clique conjectureNarrower topic: The conjecture is a geometric Ramsey-type demand for one of two contrasting structures.Burr–Erdős conjectureNarrower topic: The conjecture is a sparse-graph problem within this broader area.Combinatorial principlesNarrower topic: It uses counting and pigeonhole reasoning to prove unavoidable patterns.Erdős–Gyárfás conjectureNarrower topic: The conjecture is a specific unavoidable-substructure problem in graph theory.Friends and strangers theoremNarrower topic: The six-person result is the smallest nontrivial instance of its general existence principle.
KnowraRamsey theoryLinked fromLinked fromThe 19 pages that link to Ramsey theory, each with the reason it gives.All 19Broader topic 2Related 6Narrower topic 11Paul ErdősRelated: Erdős developed foundational results about unavoidable patterns in large combinatorial systems.Probabilistic methodRelated: Random graphs give lower bounds on how large Ramsey numbers must be.Schur's theoremNarrower topic: Schur's theorem is an early finite-coloring result in additive Ramsey theory.Extremal combinatoricsRelated: Its guarantees often identify unavoidable substructures in large colored or dense objects.Ramsey's theoremNarrower topic: The theorem gives the field its central principle of finding order in arbitrary colorings.Frank P. RamseyBroader topic: His theorem on arithmetic progressions helped establish a mathematical field bearing his name.Richard RadoNarrower topic: Rado’s theorems helped establish the field’s central questions about unavoidable structure.Paris–Harrington theoremNarrower topic: The theorem is a finitary result in this broader area.Turán's theoremRelated: Turán bounds help quantify how many edges can remain without a prescribed clique.Erdős–Stone theoremRelated: Extremal bounds from the theorem can feed into arguments that force monochromatic graph structure.Hales–Jewett theoremNarrower topic: The theorem exemplifies the principle that disorder forces a monochromatic pattern.Erdős–Rado theoremNarrower topic: The theorem provides an infinite-cardinal guarantee within Ramsey theory.Lovász local lemmaRelated: The lemma helps construct colorings that avoid specified monochromatic substructures.History of combinatoricsBroader topic: Its results reveal a characteristic modern theme: unavoidable patterns within disorder.Big-line-big-clique conjectureNarrower topic: The conjecture is a geometric Ramsey-type demand for one of two contrasting structures.Burr–Erdős conjectureNarrower topic: The conjecture is a sparse-graph problem within this broader area.Combinatorial principlesNarrower topic: It uses counting and pigeonhole reasoning to prove unavoidable patterns.Erdős–Gyárfás conjectureNarrower topic: The conjecture is a specific unavoidable-substructure problem in graph theory.Friends and strangers theoremNarrower topic: The six-person result is the smallest nontrivial instance of its general existence principle.