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). - Pontus von Brömssen, Mar 03 2022
FORMULA
a(m+n) >= a(m)*a(n).
Lim a(n)^(1/n) >= 3^(4/9).
EXAMPLE
All graphs with at most three nodes are chordal, so a(n) = 1 for n <= 3 and any graph will be optimal (containing 1 maximal chordal subgraph).
For 4 <= n <= 9, the following graphs are optimal:
n = 4: the 4-cycle;
n = 5: the 5-cycle and the complete bipartite graph K_{2,3};
n = 6: the 3-prism graph and the octahedral graph;
n = 7: the 3-prism graph with one edge (not in a triangle) subdivided by an additional node, and the complete tripartite graph K_{2,2,3};
n = 8: the gyrobifastigium graph;
n = 9: the Paley graph of order 9.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Mar 08 2021
STATUS
approved