A342213 - OEIS

%I #21 Mar 18 2022 00:14:12

%S 1,1,1,1,5,15,35,70,126,211

%N Largest number of maximal planar node-induced subgraphs of an n-node graph.

%C This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n). - _Pontus von Brömssen_, Mar 03 2022

%C a(11) >= 381, because the complete 5-partite graph K_{1,1,3,3,3} has 381 maximal planar subgraphs.

%F a(m+n) >= a(m)*a(n).

%F Lim_{n->oo} a(n)^(1/n) >= 381^(1/11) = 1.71644... .

%e For 4 <= n <= 9, a(n) = binomial(n,4) = A000332(n) and the complete graph is optimal, but a(10) = 211 > 210 = binomial(10,4) with the optimal graph being the complete 6-partite graph K_{1,1,1,1,3,3}. The optimal graph is unique when 5 <= n <= 10.

%Y Cf. A000332, A003094, A005470.

%Y For a list of related sequences, see cross-references in A342211.

%K nonn,more

%O 1,5

%A _Pontus von Brömssen_, Mar 05 2021