A342324 - OEIS

%I #20 Mar 18 2022 00:14:21

%S 1,1,1,4,5,12,16,36,81

%N Largest number of maximal chordal node-induced subgraphs of an n-node graph.

%C 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

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

%F Lim a(n)^(1/n) >= 3^(4/9).

%e 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).

%e For 4 <= n <= 9, the following graphs are optimal:

%e   n = 4: the 4-cycle;

%e   n = 5: the 5-cycle and the complete bipartite graph K_{2,3};

%e   n = 6: the 3-prism graph and the octahedral graph;

%e   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};

%e   n = 8: the gyrobifastigium graph;

%e   n = 9: the Paley graph of order 9.

%Y Cf. A048192, A048193.

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

%K nonn,more

%O 1,4

%A _Pontus von Brömssen_, Mar 08 2021