OFFSET
0,6
COMMENTS
Covering means there are no isolated vertices. Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b. A graph is topologically connected if the graph whose vertices are the edges and whose edges are crossing pairs of edges is connected.
EXAMPLE
The a(4) = 1 through a(6) = 22 edge-sets:
{13,24} {13,14,25} {13,25,46}
{13,24,25} {14,25,36}
{13,24,35} {14,26,35}
{14,24,35} {15,24,36}
{14,25,35} {13,14,15,26}
{13,14,25,26}
{13,15,24,26}
{13,15,26,46}
{13,24,25,26}
{13,24,25,36}
{13,24,26,35}
{13,24,35,36}
{13,24,35,46}
{14,15,26,36}
{14,24,35,36}
{14,24,35,46}
{14,25,35,46}
{15,24,35,46}
{15,25,35,46}
{15,25,36,46}
{15,26,35,46}
{15,26,36,46}
MATHEMATICA
croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x<z<y<t||z<x<t<y];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
crosscmpts[stn_]:=csm[Union[Subsets[stn, {1}], Select[Subsets[stn, {2}], croXQ]]];
Table[Length[fasmin[Select[Subsets[Subsets[Range[n], {2}]], And[Union@@#==Range[n], Length[crosscmpts[#]]<=1]&]]], {n, 0, 5}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 29 2019
STATUS
approved