# Viable graphs with <=13 edges for the Kontsevich conjecture.
# gr[n,k] is the list of connected graphs with n vertices, k edges,
# no cut vertex, no edge cutset of size 2, and no triple of vertices
# satisfying N(u) \subseteq N(v),V(v').
# N.B.: gr[8,12][1] is the cube, gr[8,12][4] is the twisted cube.

gr[5,8]:=[{{1,4},{2,4},{1,3},{2,3},{1,5},{2,5},{3,5},{4,5}}]:

gr[6,9]:=[{{1,4},{3,4},{2,3},{1,5},{2,5},{4,5},{1,6},{2,6},{3,6}},
{{1,4},{2,4},{3,4},{1,5},{2,5},{3,5},{1,6},{2,6},{3,6}}]:

gr[6,10]:=[{{1,4},{2,4},{1,3},{2,3},{1,5},{2,5},{4,5}
,{1,6},{2,6},{3,6}},{{1,4},{2,4},{3,4},{1,2},{1,5},{2,5},{3
,5},{1,6},{2,6},{3,6}},{{1,4},{3,4},{1,2},{2,3},{1,5},{2,5}
,{4,5},{1,6},{2,6},{3,6}},{{1,4},{3,4},{2,3},{1,5},{2,5},{1
,6},{2,6},{3,6},{4,6},{5,6}}]:

gr[6,11]:=[{{1,4},{2,4},{4,6},{5,6},{1,5},{2,5},{1,3},{2,3},{2,6},
{3,6},{1,6}},{{3,4},{1,4},{2,4},{1,5},{2,5},{1,3},{2,3},{4,5},
{2,6},{3,6},{1,6}},{{3,4},{1,4},{2,4},{5,6},{3,5},{1,2},{1,3},
{2,3},{4,5},{2,6},{1,6}}]:

gr[7,11]:=[{{1,4},{3,4},{1,5},{2,5},{4,5},{1,7},{2,7},{3,7},{1,6},
{2,6},{3,6}},{{1,4},{3,4},{2,3},{1,5},{3,5},{1,7},{2,7},{4,7},{1,6},
{2,6},{5,6}},{{1,4},{3,4},{2,3},{1,5},{3,5},{4,5},{1,7},{2,7},{6,7},
{1,6},{2,6}},{{1,4},{2,3},{1,5},{3,5},{4,5},{1,7},{2,7},{3,7},{1,6},
{2,6},{4,6}}]:

gr[6,12]:=[{{1,4},{2,4},{4,6},{1,5},{2,5},{3,5},{1,3},{2,3},{4,5},
{2,6},{3,6},{1,6}}]:

gr[7,12]:=[{{3,4},{2,4},{6,7},{1,7},{2,7},{1,5},{3,5},{1,3},
{2,3},{4,5},{2,6},{1,6}},{{1,4},{1,7},{2,7},{3,7},{4,6},{1,5},
{3,5} ,{1,2},{2,3},{4,5},{2,6},{1,6}},{{1,4},{2,4},{1,7},{2,7},
{3,7},{1,5},{2,5},{1,3},{4,5},{2,6},{3,6},{1,6}},{{3,4},{1,4}
,{1,7},{2,7},{3,7},{1,5},{2,5},{2,3},{4,5},{2,6},{3,6},{1,6
}},{{1,7},{2,7},{4,7},{4,6},{2,5},{3,5},{1,2},{1,3},{2,3},{4
,5},{3,6},{1,6}},{{3,4},{1,4},{1,7},{2,7},{4,7},{5,6},{1,5}
,{3,5},{1,2},{2,3},{2,6},{1,6}},{{2,4},{1,7},{2,7},{3,7},{4
,6},{1,5},{3,5},{1,3},{2,3},{4,5},{2,6},{1,6}},{{3,4},{1,4}
,{1,7},{2,7},{3,7},{1,5},{2,5},{1,2},{4,5},{2,6},{3,6},{1,6
}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{1,5},{2,5},{3,5},{2
,6},{3,6},{1,6}},{{3,4},{1,7},{2,7},{4,7},{5,6},{3,5},{1,2}
,{1,3},{2,3},{4,5},{2,6},{1,6}},{{3,4},{2,4},{1,7},{2,7},{4
,7},{5,6},{1,5},{3,5},{1,3},{2,3},{2,6},{1,6}},{{3,4},{1,7}
,{2,7},{3,7},{4,6},{1,5},{2,5},{1,3},{2,3},{4,5},{2,6},{1,6
}},{{3,4},{2,4},{5,7},{6,7},{1,7},{2,7},{3,7},{4,7},{1,5},{3
,5},{2,6},{1,6}},{{3,4},{5,7},{1,7},{2,7},{4,6},{2,5},{1,2}
,{1,3},{2,3},{4,5},{3,6},{1,6}},{{3,4},{1,7},{2,7},{4,7},{5
,6},{2,5},{1,2},{1,3},{2,3},{4,5},{3,6},{1,6}}]:

gr[8,12]:=[{{5,8},{6,8},{7,8},{1,4},{1,2},{1,3},{2,5},{3,5},
{3,7},{4,7},{2,6},{4,6}},{{5,8},{6,8},{7,8},{1,4},{1,2},{1,3},
{2,3},{2,5},{4,5},{4,7},{6,7},{3,6}},{{4,8},{5,8},{6,8},{1,4},
{1,2},{1,3},{2,3},{2,5},{4,7},{5,7},{6,7},{3,6}},{{4,8},{5,8},
{7,8},{1,4},{1,2},{1,3},{2,5},{3,5},{3,7},{6,7},{2,6},{4,6}}]:

gr[7,13]:=[{{2,4},{5,7},{6,7},{1,7},{2,7},{3,7},{4,7},{1,5},
{1,2},{2,3},{4,5},{3,6},{1,6}},{{1,4},{2,4},{1,7},{2,7},{3,7},
{4,6},{1,5},{3,5},{1,3},{2,3},{4,5},{2,6},{1,6}},{{3,4},{1,4},
{1,7},{2,7},{3,7},{4,6},{2,5},{3,5},{1,2},{1,3},{4,5},{2,6},{
1,6}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{5,6},{1,5},{1,3}
,{2,3},{4,5},{2,6},{1,6}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3
,7},{4,6},{5,6},{1,5},{2,5},{3,5},{2,3},{1,6}},{{1,4},{2,4}
,{1,7},{2,7},{3,7},{1,5},{2,5},{1,3},{2,3},{4,5},{2,6},{3,6
},{1,6}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{1,5},{2,5},{1
,3},{4,5},{2,6},{3,6},{1,6}},{{3,4},{1,4},{2,4},{5,7},{1,7}
,{2,7},{4,6},{5,6},{1,5},{1,2},{1,3},{2,3},{3,6}},{{3,4},{1
,4},{1,7},{2,7},{3,7},{1,5},{2,5},{1,2},{2,3},{4,5},{2,6},{
3,6},{1,6}},{{1,4},{2,4},{6,7},{1,7},{3,7},{4,6},{1,5},{2,5}
,{3,5},{1,3},{2,3},{4,5},{2,6}},{{3,4},{1,4},{2,4},{1,7},{2
,7},{4,7},{5,6},{1,5},{2,5},{3,5},{2,3},{3,6},{1,6}},{{3,4}
,{1,4},{2,4},{1,7},{2,7},{3,7},{1,5},{2,5},{3,5},{4,5},{2,6
},{3,6},{1,6}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{1,5},{2
,5},{3,5},{1,2},{2,6},{3,6},{1,6}},{{3,4},{1,4},{2,4},{2,7}
,{3,7},{4,7},{5,6},{1,5},{3,5},{1,2},{1,3},{2,6},{1,6}},{{3
,4},{1,4},{1,7},{2,7},{3,7},{4,6},{1,5},{2,5},{3,5},{2,3},{
4,5},{2,6},{1,6}},{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{4,6}
,{5,6},{2,5},{3,5},{1,2},{1,3},{1,6}},{{3,4},{2,4},{1,7},{2
,7},{4,7},{5,6},{1,5},{3,5},{1,2},{1,3},{2,3},{2,6},{1,6}},
{{3,4},{1,4},{2,4},{1,7},{2,7},{3,7},{5,6},{3,5},{1,2},{1,3}
,{4,5},{2,6},{1,6}},{{3,4},{1,4},{5,7},{6,7},{1,7},{2,7},{3
,7},{4,7},{1,5},{2,5},{2,3},{2,6},{1,6}},{{1,4},{2,4},{6,7}
,{1,7},{2,7},{4,6},{1,5},{2,5},{3,5},{1,3},{2,3},{4,5},{3,6
}},{{3,4},{1,4},{2,4},{5,7},{1,7},{2,7},{5,6},{1,2},{1,3},{2
,3},{4,5},{3,6},{1,6}},{{3,4},{1,4},{2,4},{6,7},{1,7},{2,7}
,{1,5},{2,5},{3,5},{2,3},{4,5},{3,6},{1,6}}]:

gr[8,13]:=[{{4,8},{3,8},{6,8},{7,8},{2,4},{1,2},{1,3},{3
,5},{4,5},{2,7},{5,7},{6,7},{1,6}},{{3,8},{5,8},{6,8},{7,8}
,{2,4},{1,2},{1,3},{3,5},{4,5},{2,7},{4,7},{6,7},{1,6}},{{4
,8},{5,8},{6,8},{7,8},{1,4},{1,2},{1,3},{2,3},{2,5},{4,7},{
5,7},{6,7},{3,6}},{{4,8},{5,8},{6,8},{7,8},{1,4},{1,2},{1,3}
,{2,3},{4,5},{2,7},{3,7},{6,7},{5,6}},{{4,8},{5,8},{6,8},{7
,8},{2,4},{3,4},{1,2},{1,3},{1,5},{2,7},{3,7},{6,7},{5,6}},
{{4,8},{5,8},{6,8},{7,8},{2,4},{1,2},{1,3},{3,5},{1,7},{2,7}
,{3,7},{4,6},{5,6}},{{3,8},{6,8},{7,8},{2,4},{1,2},{1,3},{4
,5},{1,7},{4,7},{5,7},{2,8},{3,6},{5,6}},{{4,8},{5,8},{6,8}
,{7,8},{1,4},{1,2},{1,3},{2,3},{2,5},{3,7},{5,7},{6,7},{4,6
}},{{3,8},{5,8},{6,8},{7,8},{2,4},{3,4},{1,2},{1,3},{1,5},{2
,7},{4,7},{6,7},{5,6}},{{3,8},{5,8},{6,8},{7,8},{1,4},{1,2}
,{1,3},{2,3},{4,5},{2,7},{4,7},{6,7},{5,6}},{{4,8},{5,8},{6
,8},{7,8},{2,4},{1,2},{1,3},{3,5},{4,5},{2,7},{3,7},{6,7},{
1,6}},{{3,8},{5,8},{6,8},{7,8},{1,2},{1,3},{2,3},{4,5},{1,7}
,{2,7},{4,7},{4,6},{5,6}},{{4,8},{5,8},{6,8},{7,8},{1,4},{3
,4},{1,2},{1,3},{2,5},{3,7},{5,7},{6,7},{2,6}},{{3,8},{6,8}
,{7,8},{2,4},{1,2},{1,3},{3,5},{1,7},{4,7},{5,7},{2,8},{4,6
},{5,6}},{{4,8},{5,8},{6,8},{7,8},{1,4},{2,4},{1,3},{2,3},{1
,5},{3,7},{5,7},{6,7},{2,6}},{{4,8},{5,8},{6,8},{7,8},{2,4}
,{3,4},{1,2},{1,3},{1,5},{3,7},{5,7},{6,7},{2,6}},{{4,8},{3
,8},{5,8},{6,8},{1,2},{1,3},{2,3},{4,5},{1,7},{2,7},{5,7},{
6,7},{4,6}},{{4,8},{3,8},{5,8},{6,8},{1,4},{1,2},{1,3},{2,5}
,{3,7},{4,7},{5,7},{6,7},{2,6}},{{4,8},{3,8},{5,8},{6,8},{2
,4},{1,2},{1,3},{3,5},{1,7},{2,7},{5,7},{6,7},{4,6}},{{4,8}
,{3,8},{5,8},{6,8},{1,4},{1,2},{2,3},{1,5},{2,7},{4,7},{5,7
},{6,7},{3,6}},{{4,8},{5,8},{6,8},{2,4},{1,2},{1,3},{3,5},{1
,7},{3,7},{5,7},{6,7},{2,8},{4,6}},{{4,8},{3,8},{5,8},{6,8}
,{1,4},{1,2},{1,3},{2,5},{2,7},{4,7},{5,7},{6,7},{3,6}},{{4
,8},{3,8},{5,8},{6,8},{1,4},{1,2},{1,3},{2,3},{2,7},{4,7},{
5,7},{6,7},{5,6}},{{4,8},{3,8},{5,8},{6,8},{2,4},{3,4},{1,2}
,{1,3},{1,7},{2,7},{5,7},{6,7},{5,6}},{{3,8},{5,8},{6,8},{2
,4},{1,2},{1,3},{3,5},{1,7},{4,7},{5,7},{6,7},{2,8},{4,6}},
{{3,8},{5,8},{6,8},{2,4},{3,4},{1,2},{1,3},{1,7},{4,7},{5,7}
,{6,7},{2,8},{5,6}},{{4,8},{3,8},{5,8},{6,8},{7,8},{1,4},{1
,3},{2,3},{1,5},{2,7},{5,7},{2,6},{4,6}},{{4,8},{3,8},{5,8}
,{6,8},{7,8},{2,4},{3,4},{1,2},{1,3},{1,5},{5,7},{6,7},{2,6
}},{{4,8},{3,8},{5,8},{6,8},{7,8},{1,4},{1,3},{2,3},{1,5},{4
,5},{2,7},{6,7},{2,6}},{{4,8},{3,8},{5,8},{6,8},{7,8},{1,4}
,{1,2},{1,3},{2,3},{2,5},{5,7},{6,7},{4,6}},{{4,8},{3,8},{5
,8},{6,8},{7,8},{1,4},{2,4},{1,3},{2,3},{1,5},{5,7},{6,7},{
2,6}},{{4,8},{3,8},{5,8},{6,8},{7,8},{1,4},{3,4},{1,2},{1,3}
,{2,5},{5,7},{6,7},{2,6}}]: