*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000322
-----------------------------------------------------------------------------
Collection: Graphs
-----------------------------------------------------------------------------
Description: The skewness of a graph.
For a graph $G$, the '''skewness''' of $G$ is the minimum number of edges of $G$ whose removal results in a planar graph.
-----------------------------------------------------------------------------
References: [1] Cimikowski, R. J. Graph planarization and skewness [[MathSciNet:1208914]]
[2] [[wikipedia:Planarization]]
[3] [[http://mathworld.wolfram.com/GraphSkewness.html]]
-----------------------------------------------------------------------------
Code:
@cached_function
def statistic(G):
if G.is_planar():
return 0
bound = G.size()
for e in G.edges(labels=False):
H = G.copy(immutable=False)
H.delete_edge(e)
bound = min(bound, 1+statistic(H.canonical_label().copy(immutable=True)))
return bound
-----------------------------------------------------------------------------
Statistic values:
([],1) => 0
([],2) => 0
([(0,1)],2) => 0
([],3) => 0
([(1,2)],3) => 0
([(0,2),(1,2)],3) => 0
([(0,1),(0,2),(1,2)],3) => 0
([],4) => 0
([(2,3)],4) => 0
([(1,3),(2,3)],4) => 0
([(0,3),(1,3),(2,3)],4) => 0
([(0,3),(1,2)],4) => 0
([(0,3),(1,2),(2,3)],4) => 0
([(1,2),(1,3),(2,3)],4) => 0
([(0,3),(1,2),(1,3),(2,3)],4) => 0
([(0,2),(0,3),(1,2),(1,3)],4) => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
([],5) => 0
([(3,4)],5) => 0
([(2,4),(3,4)],5) => 0
([(1,4),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,4),(3,4)],5) => 0
([(1,4),(2,3)],5) => 0
([(1,4),(2,3),(3,4)],5) => 0
([(0,1),(2,4),(3,4)],5) => 0
([(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,3),(3,4)],5) => 0
([(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,3),(2,3),(2,4)],5) => 0
([(0,1),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(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) => 0
([(3,5),(4,5)],6) => 0
([(2,5),(3,5),(4,5)],6) => 0
([(1,5),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
([(2,5),(3,4)],6) => 0
([(2,5),(3,4),(4,5)],6) => 0
([(1,2),(3,5),(4,5)],6) => 0
([(3,4),(3,5),(4,5)],6) => 0
([(1,5),(2,5),(3,4),(4,5)],6) => 0
([(0,1),(2,5),(3,5),(4,5)],6) => 0
([(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4)],6) => 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3)],6) => 0
([(1,5),(2,4),(3,4),(3,5)],6) => 0
([(0,1),(2,5),(3,4),(4,5)],6) => 0
([(1,2),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 0
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 0
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 0
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 0
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(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),(3,4),(4,5),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 0
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 0
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 0
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 0
([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 0
([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 0
([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 0
([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 0
([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 0
([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 0
([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 0
([(0,9),(1,9),(2,8),(3,8),(4,7),(5,7),(6,9),(6,10),(7,10),(8,10)],11) => 0
([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11) => 0
([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 0
([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 0
([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 0
([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 0
([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 0
([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 0
([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 0
([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13) => 0
([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 0
([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 0
([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13) => 0
-----------------------------------------------------------------------------
Created: Dec 09, 2015 at 11:47 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Dec 23, 2020 at 22:20 by Martin Rubey