Values
=>
Cc0020;cc-rep
([],1)=>0
([],2)=>2
([(0,1)],2)=>1
([],3)=>3
([(1,2)],3)=>2
([(0,2),(1,2)],3)=>2
([(0,1),(0,2),(1,2)],3)=>2
([],4)=>3
([(2,3)],4)=>3
([(1,3),(2,3)],4)=>3
([(0,3),(1,3),(2,3)],4)=>3
([(0,3),(1,2)],4)=>4
([(0,3),(1,2),(2,3)],4)=>3
([(1,2),(1,3),(2,3)],4)=>3
([(0,3),(1,2),(1,3),(2,3)],4)=>2
([(0,2),(0,3),(1,2),(1,3)],4)=>4
([(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)=>3
([],5)=>4
([(3,4)],5)=>3
([(2,4),(3,4)],5)=>3
([(1,4),(2,4),(3,4)],5)=>4
([(0,4),(1,4),(2,4),(3,4)],5)=>3
([(1,4),(2,3)],5)=>4
([(1,4),(2,3),(3,4)],5)=>3
([(0,1),(2,4),(3,4)],5)=>5
([(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,4),(2,3),(3,4)],5)=>4
([(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(1,3),(1,4),(2,3),(2,4)],5)=>4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>3
([(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)=>5
([(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)=>4
([(0,1),(2,3),(2,4),(3,4)],5)=>6
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>5
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4
([(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)=>4
([(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)=>3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(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)=>4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([],6)=>4
([(4,5)],6)=>4
([(3,5),(4,5)],6)=>4
([(2,5),(3,5),(4,5)],6)=>4
([(1,5),(2,5),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
([(2,5),(3,4)],6)=>4
([(2,5),(3,4),(4,5)],6)=>3
([(1,2),(3,5),(4,5)],6)=>5
([(3,4),(3,5),(4,5)],6)=>4
([(1,5),(2,5),(3,4),(4,5)],6)=>4
([(0,1),(2,5),(3,5),(4,5)],6)=>5
([(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,5),(1,5),(2,4),(3,4)],6)=>5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>4
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(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)=>5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(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)=>5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(2,3)],6)=>4
([(1,5),(2,4),(3,4),(3,5)],6)=>4
([(0,1),(2,5),(3,4),(4,5)],6)=>5
([(1,2),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>5
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>5
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>7
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>5
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>6
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>6
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>6
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>5
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>5
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>5
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>4
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(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)=>5
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>9
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>6
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>8
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>7
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>7
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>6
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>5
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>7
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>6
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(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)=>4
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(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)=>4
([(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)=>4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(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)=>4
([(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)=>6
([(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)=>5
([(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)=>5
([(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)=>5
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Description
The disjunction number of a graph.
Let $V_n$ be the power set of $\{1,\dots,n\}$ and let $E_n=\{(a,b)| a,b\in V_n, a\neq b, a\cap b=\emptyset\}$. Then the disjunction number of a graph $G$ is the smallest integer $n$ such that $(V_n, E_n)$ has an induced subgraph isomorphic to $G$.
Let $V_n$ be the power set of $\{1,\dots,n\}$ and let $E_n=\{(a,b)| a,b\in V_n, a\neq b, a\cap b=\emptyset\}$. Then the disjunction number of a graph $G$ is the smallest integer $n$ such that $(V_n, E_n)$ has an induced subgraph isomorphic to $G$.
References
[1] van der Zypen, D. Disjunction number of a graph MathOverflow:331366
Code
def Dominics_graph(n):
V = map(frozenset, powerset(range(n)))
return Graph([V, lambda a, b: a != b and a.isdisjoint(b)])
def statistic(G):
n = 0
while True:
H = Dominics_graph(n)
H.relabel()
if H.subgraph_search(G, induced=True):
return n
n += 1
Created
May 13, 2019 at 08:43 by Martin Rubey
Updated
May 14, 2019 at 12:51 by Martin Rubey
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