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 A342324 Largest number of maximal chordal node-induced subgraphs of an n-node graph. 3

%I

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

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

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

%F liminf 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 of the "long" edges subdivided by an additional node, and the complete graph with one triangle and two edges (pairwise node-disjoint) removed;

%e n = 8: the gyrobifastigium graph;

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

%Y Cf. A342211, A342212, A342213.

%K nonn,more

%O 1,4

%A _Pontus von Brömssen_, Mar 08 2021

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Last modified August 1 03:05 EDT 2021. Contains 346379 sequences. (Running on oeis4.)