Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000479
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Mapping
St000479: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 2
([],3)
 => 3
([(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => 3
([(0,1),(0,2),(1,2)],3)
 => 6
([],4)
 => 4
([(2,3)],4)
 => 4
([(1,3),(2,3)],4)
 => 4
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 5
([(0,3),(1,2),(2,3)],4)
 => 5
([(1,2),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,2),(0,3),(1,2),(1,3)],4)
 => 6
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 10
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 18
([],5)
 => 5
([(3,4)],5)
 => 5
([(2,4),(3,4)],5)
 => 5
([(1,4),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 7
([(1,4),(2,3)],5)
 => 5
([(1,4),(2,3),(3,4)],5)
 => 5
([(0,1),(2,4),(3,4)],5)
 => 6
([(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,3),(3,4)],5)
 => 6
([(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(1,3),(1,4),(2,3),(2,4)],5)
 => 6
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 6
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 9
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 10
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,4),(1,3),(2,3),(2,4)],5)
 => 6
([(0,1),(2,3),(2,4),(3,4)],5)
 => 7
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 9
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 10
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 18
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 18
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 18
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 10
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 15
Description
The Ramsey number of a graph. This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1] Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]