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A342324 Largest number of maximal chordal node-induced subgraphs of an n-node graph. 3
1, 1, 1, 4, 5, 12, 16, 36, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..9.

FORMULA

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

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

  n = 8: the gyrobifastigium graph;

  n = 9: the Paley graph of order 9.

CROSSREFS

Cf. A342211, A342212, A342213.

Sequence in context: A269227 A103650 A131116 * A261692 A131328 A054451

Adjacent sequences:  A342321 A342322 A342323 * A342325 A342326 A342327

KEYWORD

nonn,more

AUTHOR

Pontus von Brömssen, Mar 08 2021

STATUS

approved

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)