A371162 -id:A371162 - cp's OEIS frontend

A376782 Triangle read by rows: T(n,m) is the number of unlabeled graphs with n vertices having m minimum forbidden subgraphs, n >= 1, 1 <= m <= A371162(n).

1, 1, 1, 1, 3, 1, 4, 4, 2, 1, 4, 8, 13, 8, 1, 4, 5, 7, 20, 34, 31, 28, 12, 8, 5, 0, 1, 1, 4, 5, 13, 26, 33, 43, 59, 50, 62, 58, 60, 64, 67, 63, 70, 68, 65, 61, 60, 31, 28, 16, 8, 13, 4, 4, 4, 0, 2, 1, 0, 1, 1, 4, 6, 9, 21, 34, 39, 71, 74, 77, 99, 118, 124, 107, 129

Offset: 1

Max Alekseyev, Oct 03 2024

			Triangle starts with
n = 1: 1
n = 2: 1 1
n = 3: 1 3
n = 4: 1 4 4  2
n = 5: 1 4 8 13  8
n = 6: 1 4 5  7 20 34 31 28 12 8 5 0 1
...

Max Alekseyev, Table of k, a(k) for k = 1..209 (rows n = 1..8 flattened)
Max A. Alekseyev and Allan Bickle, Forbidden Subgraphs of Single Graphs, 2024.

Cf. A000088 (row sums), A371162 (row lengths), A000012 (column m=1), A113311 (column m=2).

Cf. A002865, A006897, A103221, A371161, A376780, A376781.

A371161 Maximum number of unlabeled graphs with at most n nodes such that neither one is a subgraph of another.

Original entry on oeis.org

1, 1, 1, 2, 3, 7, 26, 157, 1687

Offset: 0

Max Alekseyev, Mar 13 2024

Width of the poset of unlabeled graphs of order at most n with the subgraph relationship.

a(n) >= A000717(n).

Cf. A000717, A006897, A371162.

A376780 Triangular table read by rows: T(n,k) is the minimum number of minimal forbidden subgraphs of a graph with n vertices and k edges, n >= 1, 0 <= k <= n*(n-1)/2.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 3, 2, 2, 1, 2, 3, 2, 3, 3, 4, 3, 3, 2, 2, 1, 2, 3, 3, 2, 4, 3, 4, 5, 5, 4, 5, 5, 4, 2, 2, 1, 2, 3, 3, 2, 4, 4, 3, 4, 5, 4, 5, 5, 7, 6, 6, 5, 5, 4, 4, 2, 2, 1, 2, 3, 3, 3, 2, 4, 4, 3, 5, 6, 5, 6, 5, 5, 7, 6, 7, 10, 9, 9, 9, 8, 10, 5, 5, 4, 2, 2, 1

Offset: 1

Max Alekseyev, Oct 03 2024

			Table starts with
n = 1: 1
n = 2: 2, 1
n = 3: 2, 2, 2, 1
n = 4: 2, 3, 2, 3, 2, 2, 1
...

Max A. Alekseyev and Allan Bickle, Forbidden Subgraphs of Single Graphs, 2024.

Cf. A002865, A006897, A103221, A371161, A371162, A376781, A376782.

A376781 Triangular table read by rows: T(n,k) is the maximum number of minimal forbidden subgraphs of a graph with n vertices and k edges, n >= 1, 0 <= k <= n*(n-1)/2.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 1, 2, 3, 4, 4, 3, 2, 1, 2, 3, 4, 5, 5, 5, 5, 4, 3, 2, 1, 2, 3, 4, 6, 8, 8, 9, 13, 11, 11, 9, 6, 5, 3, 2, 1, 2, 3, 4, 6, 8, 8, 11, 16, 20, 23, 28, 31, 30, 33, 24, 22, 15, 10, 7, 3, 2, 1, 2, 3, 4, 6, 8, 9, 14, 21, 24, 31, 41, 57, 78, 86, 106, 123, 134, 149, 143, 138, 133, 75, 46, 37, 18, 11, 3, 2, 1

Offset: 1

Max Alekseyev, Oct 03 2024

			Table starts with
n = 1: 1
n = 2: 2, 1
n = 3: 2, 2, 2, 1
n = 4: 2, 3, 4, 4, 3, 2, 1
...

Max A. Alekseyev and Allan Bickle, Forbidden Subgraphs of Single Graphs, 2024.

Cf. A371162 (row maximums).

Cf. A002865, A006897, A103221, A371161, A376780, A376782.

cp's OEIS Frontend

A376782 Triangle read by rows: T(n,m) is the number of unlabeled graphs with n vertices having m minimum forbidden subgraphs, n >= 1, 1 <= m <= A371162(n).

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A371161 Maximum number of unlabeled graphs with at most n nodes such that neither one is a subgraph of another.

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A376780 Triangular table read by rows: T(n,k) is the minimum number of minimal forbidden subgraphs of a graph with n vertices and k edges, n >= 1, 0 <= k <= n*(n-1)/2.

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A376781 Triangular table read by rows: T(n,k) is the maximum number of minimal forbidden subgraphs of a graph with n vertices and k edges, n >= 1, 0 <= k <= n*(n-1)/2.

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