OFFSET
1,4
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) >= 64^(1/9) = 1.58740... .
EXAMPLE
All graphs with at most three nodes are cographs, so a(n) = 1 for n <= 3 and any graph is optimal.
All optimal graphs (i.e., graphs that have n nodes and a(n) maximal cographical subgraphs) for 4 <= n <= 9 are listed below. Since a graph is a cograph if and only if its complement is a cograph, the optimal graphs come in complementary pairs.
n = 4: the path of length 3 (self-complementary);
n = 5: the 5-cycle (self-complementary);
n = 6: the Hajós graph (also known as a Sierpiński sieve graph) and its complement;
n = 7: the elongated triangular pyramid and its complement;
n = 8: the Möbius ladder and its complement (the antiprism graph);
n = 9: the pentagonal bipyramid with an additional path of length 3 between the two apex nodes (self-complementary).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Mar 08 2022
STATUS
approved