A352215 Largest number of maximal C_4-free node-induced subgraphs of an n-node graph.

1, 1, 1, 4, 5, 12, 16, 32, 54

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).

Examples

			All graphs with at most three nodes are C_4-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 C_4-free subgraphs:
  n = 4: the 4-cycle;
  n = 5: K_{2,3};
  n = 6: the prism graph and the octahedral graph;
  n = 7: the complement of 2*K_2 + K_3;
  n = 8: K_4 X K_2 (Cartesian product) and the 16-cell;
  n = 9: the circulant graph C_9(1,3), and K_{3,3,3} with three edges removed, one edge between the first and second parts in the partition and two edges from two other nodes in these two parts to a node in the third part.
		

Crossrefs

Cf. A079566, A352068.

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) >= 54^(1/9) = 1.55771... .