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 A326341 Number of minimal topologically connected chord graphs covering {1..n}. 3
 1, 0, 1, 0, 1, 5, 22, 119 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Table of n, a(n) for n=0..7. 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_, ___}, ___}/; x0]&]}, 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}] CROSSREFS The non-minimal case is A324327. Minimal covers are A053530. Topologically connected graphs are A324327 (covering) or A324328 (all). Cf. A000108, A006125, A007297, A054726, A136653, A324169, A326210, A326293. Sequence in context: A020003 A276750 A131460 * A062794 A036235 A159596 Adjacent sequences: A326338 A326339 A326340 * A326342 A326343 A326344 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 29 2019 STATUS approved

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Last modified July 24 02:09 EDT 2024. Contains 374575 sequences. (Running on oeis4.)