- FindStat

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Identifier

St000537: Graphs ⟶ ℤ

Values

([],1) => 0

([],2) => 0

([(0,1)],2) => 1

([],3) => 0

([(1,2)],3) => 1

([(0,2),(1,2)],3) => 1

([(0,1),(0,2),(1,2)],3) => 2

([],4) => 0

([(2,3)],4) => 1

([(1,3),(2,3)],4) => 1

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

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

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

([(1,2),(1,3),(2,3)],4) => 2

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

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

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

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

([],5) => 0

([(3,4)],5) => 1

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

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

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

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

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

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

([(2,3),(2,4),(3,4)],5) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],6) => 0

([(4,5)],6) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The cutwidth of a graph.
This is the minimum possible width of a linear ordering of its vertices, where the width of an ordering $\sigma$ is the maximum, among all the prefixes of $\sigma$, of the number of edges that have exactly one vertex in a prefix.

References

[1] wikipedia:Pathwidth

Code

from sage.graphs.graph_decompositions.cutwidth import cutwidth

def statistic(G):
    return cutwidth(G)[0]

Created

Jun 21, 2016 at 07:55 by Martin Rubey

Updated

Jan 17, 2022 at 14:07 by Martin Rubey