Ramsey's theorem for numbers
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complete graphs
|
| gptkbp:category |
theorems in discrete mathematics
|
| gptkbp:concerns |
edge colorings
monochromatic subgraphs |
| gptkbp:field |
combinatorics
|
| gptkbp:firstPublished |
1930
|
| gptkbp:generalizes |
gptkb:van_der_Waerden's_theorem
gptkb:Schur's_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Ramsey's theorem for numbers
|
| gptkbp:influenced |
gptkb:Erdős–Szekeres_theorem
gptkb:Ramsey's_theorem_for_hypergraphs |
| gptkbp:namedAfter |
gptkb:Frank_P._Ramsey
|
| gptkbp:parameter |
gptkb:Ramsey_number
|
| gptkbp:relatedTo |
gptkb:Ramsey_theory
|
| gptkbp:sentence |
For any given positive integers k and r, there exists a minimum number R(k, r) such that any coloring of the edges of a complete graph of order R(k, r) with r colors contains a monochromatic complete subgraph of order k.
|
| gptkbp:bfsParent |
gptkb:Ramsey_theory
|
| gptkbp:bfsLayer |
5
|