A352212 Largest number of maximal triangle-free node-induced subgraphs of an n-node graph.

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.

Links

Table of n, a(n) for n=1..9.

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

Cf. A000217, A006785, A024607.

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

Sequence in context: A346735 A174163 A152899 * A342212 A061304 A109442

Adjacent sequences: A352209 A352210 A352211 * A352213 A352214 A352215

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 08 2022

Status

approved