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A352212
Largest number of maximal triangle-free node-induced subgraphs of an n-node graph.
1
1, 1, 3, 6, 10, 15, 21, 36, 60
OFFSET
1,3
COMMENTS
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).
Assuming that there exists a disconnected optimal graph for n >= 8 (this is the case for n = 8 and n = 9), it would hold that a(10) = 100, a(11) = 150, a(12) = 225, and a(n) = 10*a(n-5) for n >= 13.
FORMULA
a(m+n) >= a(m)*a(n).
Limit_{n->oo} a(n)^(1/n) >= 10^(1/5) = 1.58489... .
EXAMPLE
For 2 <= n <= 7, a(n) = binomial(n,2) = A000217(n-1) and the complete graph is optimal (it is the unique optimal graph for 3 <= n <= 7), but a(8) = 36 > binomial(8,2), with the optimal graphs being K_4 + K_4, with up to 4 additional node-disjoint edges. For n = 9 the optimal graphs are K_4 + K_5 with up to 4 additional node-disjoint edges.
CROSSREFS
For a list of related sequences, see cross-references in A342211.
Sequence in context: A346735 A174163 A152899 * A342212 A061304 A109442
KEYWORD
nonn,more
AUTHOR
STATUS
approved