A352210
Largest number of maximal 2-degenerate node-induced subgraphs of an n-node graph.
Original entry on oeis.org
1, 1, 1, 4, 10, 20, 35, 56, 97
Offset: 1
For 3 <= n <= 8, a(n) = binomial(n,3) = A000292(n-2) and the complete graph is optimal, but a(9) = 97 > binomial(9,3) with the optimal graph being the complement of the disjoint union of K_3 and K_{3,3}. The optimal graph is unique when 4 <= n <= 9.
For a list of related sequences, see cross-references in
A342211.
A384849
Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with degeneracy k, 0 <= k < n.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 9, 18, 5, 1, 1, 19, 85, 43, 7, 1, 1, 36, 471, 442, 85, 8, 1, 1, 75, 3378, 6979, 1758, 144, 10, 1, 1, 152, 31782, 166258, 70811, 5421, 231, 11, 1, 1, 328, 385205, 5892753, 5164116, 547170, 15239, 342, 13, 1
Offset: 1
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 5, 4, 1;
1, 9, 18, 5, 1;
1, 19, 85, 43, 7, 1;
1, 36, 471, 442, 85, 8, 1;
1, 75, 3378, 6979, 1758, 144, 10, 1;
1, 152, 31782, 166258, 70811, 5421, 231, 11, 1;
1, 328, 385205, 5892753, 5164116, 547170, 15239, 342, 13, 1;
...
Showing 1-2 of 2 results.
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