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A326339 Number of connected simple graphs with vertices {1..n} and no crossing or nesting edges. 6
1, 0, 1, 4, 12, 36, 108, 324 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d.
Appears to be essentially the same as A003946.
LINKS
EXAMPLE
The a(2) = 1 through a(4) = 36 edge-sets:
{12} {12,13} {12,13,14}
{12,23} {12,13,34}
{13,23} {12,14,34}
{12,13,23} {12,23,24}
{12,23,34}
{12,24,34}
{13,23,34}
{14,24,34}
{12,13,14,34}
{12,13,23,34}
{12,14,24,34}
{12,23,24,34}
MATHEMATICA
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]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[csm[#]]<=1&&!MatchQ[#, {___, {x_, y_}, ___, {z_, t_}, ___}/; x<z<y<t||z<x<t<y||x<z<t<y||z<x<y<t]&]], {n, 0, 5}]
CROSSREFS
Covering graphs with no crossing or nesting edges are A326329.
Connected simple graphs are A001349.
The case with only crossing edges forbidden is A007297.
Graphs without crossing or nesting edges are A326244.
Sequence in context: A156945 A006817 A163315 * A334877 A003119 A001394
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 29 2019
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)