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A352209
Largest number of maximal perfect node-induced subgraphs of an n-node graph.
1
1, 1, 1, 1, 5, 5, 13, 18, 42
OFFSET
1,5
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).
FORMULA
a(m+n) >= a(m)*a(n).
Limit_{n->oo} a(n)^(1/n) >= 42^(1/9) = 1.51482... .
EXAMPLE
All graphs with at most four nodes are perfect, so a(n) = 1 for n <= 4 and any graph is optimal.
All optimal graphs (i.e., graphs that have n nodes and a(n) maximal perfect subgraphs) for 5 <= n <= 9 are listed below. Since a graph is perfect if and only if its complement is perfect, the optimal graphs come in complementary pairs.
n = 5: the 5-cycle;
n = 6: the wheel graph with any subset of the spokes removed (8 graphs in total);
n = 7: the chestahedral graph and its complement;
n = 8: the bislit cube graph, the snub disphenoidal graph, and their complements;
n = 9: the bislit cube graph with an additional node with edges to two neighboring nodes of degree 4 and to the two nodes of degree 3 on the opposite face of the cube, the snub disphenoidal graph with an additional node with edges to the four nodes of degree 4, and their complements.
CROSSREFS
For a list of related sequences, see cross-references in A342211.
Sequence in context: A164927 A094904 A286456 * A171663 A126439 A318541
KEYWORD
nonn,more
AUTHOR
STATUS
approved