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Largest number of maximal 2-degenerate node-induced subgraphs of an n-node graph.
1

%I #8 Mar 15 2022 05:22:54

%S 1,1,1,4,10,20,35,56,97

%N Largest number of maximal 2-degenerate 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).

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

%F Limit_{n->oo} a(n)^(1/n) >= 97^(1/9) = 1.66246... .

%e For 3 <= n <= 8, a(n) = binomial(n,3) = A000292(n-2) and the complete graph is optimal, but a(9) = 97 > binomial(9,3) with the optimal graph being the complement of the disjoint union of K_3 and K_{3,3}. The optimal graph is unique when 4 <= n <= 9.

%Y Cf. A000292, A352067.

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

%K nonn,more

%O 1,4

%A _Pontus von Brömssen_, Mar 08 2022