A326340 Number of maximal simple graphs with vertices {1..n} and no crossing or nesting edges.

1, 1, 1, 1, 4, 9, 19, 42

Offset: 0

Author

Gus Wiseman, Jun 29 2019

Keywords

• nonn
• more

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.

Links

• Gus Wiseman, The a(6) = 19 maximal non-crossing non-nesting graphs.

Crossrefs

Covering graphs with no crossing or nesting edges are A326329.

The case with only crossing edges forbidden is A000108 shifted right twice.

Simple graphs without crossing or nesting edges are A326244.

Connected graphs with no crossing or nesting edges are A326339.

Cf. A006125, A007297, A054726, A117662, A136653.

Cf. A324169, A324327, A324328, A326279, A326293.

Programs

Mathematica

fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Subsets[Range[n],{2}]],!MatchQ[#,{_,{x_,y_},_,{z_,t_},_}/;x