- FindStat

Identifier

Mp00262: Binary words —poset of factors⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St001638: Graphs ⟶ ℤ

Values

=> ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 0
=> ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => 0
=> ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 0
=> ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
=> ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
=> ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 0
=> ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 0
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 1
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 1
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1
=> ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 0
=> ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1
=> ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

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$F_{1} = 2$

$F_{2} = 2 + 2\ q$

$F_{3} = 2 + 6\ q$

Description

The book thickness of a graph.
The book thickness (or pagenumber, or stacknumber) of a graph is the minimal number of pages required for a book embedding of a graph.

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.

Map

poset of factors

Description

The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that

$u < v$ if and only if

$u$ is a factor of

$v$ .

Map

connected complement

Description

The componentwise connected complement of a graph.
For a connected graph

$G$ , this map returns the complement of

$G$ if it is connected, otherwise

$G$ itself. If

$G$ is not connected, the map is applied to each connected component separately.