Ramsey's theorem for colorings
GPTKB entity
Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
graphs
hypergraphs |
| gptkbp:field |
combinatorics
|
| gptkbp:firstPublished |
1930
|
| gptkbp:generalizes |
gptkb:pigeonhole_principle
|
| gptkbp:hasConcept |
gptkb:Ramsey_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ramsey's theorem for colorings
|
| gptkbp:namedAfter |
gptkb:Frank_P._Ramsey
|
| gptkbp:relatedTo |
gptkb:Ramsey_number
gptkb:Erdős–Szekeres_theorem gptkb:van_der_Waerden's_theorem |
| gptkbp:state |
In any coloring of the edges of a sufficiently large complete graph, there exists a monochromatic complete subgraph of a given size.
|
| gptkbp:usedIn |
gptkb:logic
number theory theoretical computer science graph theory |
| gptkbp:bfsParent |
gptkb:Ramsey_theory
|
| gptkbp:bfsLayer |
5
|