Processing math: 100%

Identifier
Values
['A',1] => ([],1) => ([],1) => ([(0,1)],2) => 2
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => 7
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 9
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searching the database for statistics with the same generating function
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 Kn contains a (not necessarily induced) monochromatic copy of the given graph. [1]
Thus, the Ramsey number of the complete graph Kn is the ordinary Ramsey number R(n,n). Very few of these numbers are known, in particular, it is only known that 43R(5,5)48. [2,3,4,5]
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where αβ if βα is a simple root.
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.