Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
theoretical computer science
graph theory |
| gptkbp:defines |
the smallest integer n such that any graph on n vertices contains either a clique of size k or an independent set of size k
|
| gptkbp:field |
combinatorics
|
| gptkbp:growthForm |
grows at least exponentially with k
|
| https://www.w3.org/2000/01/rdf-schema#label |
diagonal Ramsey number
|
| gptkbp:lowerBound |
R(k,k) ≥ 2^{k/2}
|
| gptkbp:namedAfter |
gptkb:Frank_P._Ramsey
|
| gptkbp:openProblem |
Exact values for R(k,k) for k > 4 are unknown
|
| gptkbp:property |
R(1,1) = 1
R(2,2) = 2 R(3,3) = 6 R(4,4) = 18 R(5,5) is between 43 and 49 |
| gptkbp:relatedTo |
gptkb:Ramsey_number
|
| gptkbp:studiedIn |
gptkb:Ramsey_theory
|
| gptkbp:symbol |
R(k,k)
|
| gptkbp:upperBound |
R(k,k) ≤ 4^{k}
|
| gptkbp:bfsParent |
gptkb:Ramsey_number
|
| gptkbp:bfsLayer |
5
|