A352216 Largest number of maximal diamond-free node-induced subgraphs of an n-node graph.

1, 1, 1, 4, 7, 11, 21, 36, 62

Offset: 1

Author

Pontus von Brömssen, Mar 08 2022

Keywords

• nonn
• more

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).

a(10) >= 102, because the complement of 2*C_5 has 102 maximal diamond-free subgraphs. It is likely that this is optimal.

Examples

			All graphs with at most three nodes are diamond-free, so a(n) = 1 for n <= 3 and any graph is optimal.
For 4 <= n <= 9, the following are all optimal graphs, i.e., graphs that have n nodes and a(n) maximal diamond-free subgraphs:
  n = 4: the diamond graph;
  n = 5: the wheel graph;
  n = 6: the complement of the H graph, the complement of P_3 + P_3 (the disjoint union of two paths of length 2), and the octahedral graph;
  n = 7: the complement of P_3 + P_4;
  n = 8: the complement of P_3 + C_5, and the complement of 2*P_4;
  n = 9: the complement of P_4 + C_5.
		

Crossrefs

Cf. A242790.

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

Formula

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

Limit_{n->oo} a(n)^(1/n) >= 102^(1/10) = 1.58803... .