Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
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Description
The connected partition number of a graph.
This is the maximal number of blocks of a set partition $P$ of the set of vertices of a graph such that contracting each block of $P$ to a single vertex yields a clique.
Also called the pseudoachromatic number of a graph. This is the largest $n$ such that there exists a (not necessarily proper) $n$-coloring of the graph so that every two distinct colors are adjacent.
This is the maximal number of blocks of a set partition $P$ of the set of vertices of a graph such that contracting each block of $P$ to a single vertex yields a clique.
Also called the pseudoachromatic number of a graph. This is the largest $n$ such that there exists a (not necessarily proper) $n$-coloring of the graph so that every two distinct colors are adjacent.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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.
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.
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