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Identifier

St001393: 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) => 1

([],4) => 0

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

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

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

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

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

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

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

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

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

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

([],5) => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 1

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

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

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

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

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

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

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

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

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

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

([],6) => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 1

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

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

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

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

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

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

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

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

([(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) => 2

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

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

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

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

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Description

The induced matching number of a graph.
An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.

Code

def statistic(G):
    for n in range(G.matching(value_only=True), -1, -1):
        M = Graph([(i,i+1) for i in range(0, 2*n, 2)])
        H = G.subgraph_search(M, induced=True)
        if H is not None:
            return n

Created

May 16, 2019 at 12:02 by Martin Rubey

Updated

May 16, 2019 at 12:02 by Martin Rubey