Identifier
-
Mp00046:
Ordered trees
—to graph⟶
Graphs
St001326: Graphs ⟶ ℤ
Values
[] => ([],1) => 0
[[]] => ([(0,1)],2) => 0
[[],[]] => ([(0,2),(1,2)],3) => 0
[[[]]] => ([(0,2),(1,2)],3) => 0
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 0
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 0
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 0
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 0
[[[[]]]] => ([(0,3),(1,2),(2,3)],4) => 0
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 0
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 0
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[[],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[],[[[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 0
[[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 0
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[]],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 0
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 0
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 0
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[[],[[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 0
[[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 0
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 0
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 1
[[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
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Description
The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph.
A graph is an interval graph if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge and $(a,b)$ is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
A graph is an interval graph if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge and $(a,b)$ is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
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