Identifier
Values
['A',1] => ([],1) => ([],1) => ([(0,1)],2) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
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searching the database for the individual values of this statistic
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Description
The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph.
A graph is bipartite if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,b)$ and $(b,c)$ are edges. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
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 $\alpha \prec \beta$ if $\beta - \alpha$ 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.
Map
incomparability graph
Description
The incomparability graph of a poset.