A350716 a(n) is the minimum number of vertices of degree 3 over all 3-collapsible graphs with n vertices.

4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30

Offset

4,1

Comments

A graph G is k-collapsible if it has minimum degree k and has no proper induced subgraph with minimum degree k.

Links

Paolo Xausa, Table of n, a(n) for n = 4..10000

Allan Bickle, The k-Cores of a Graph, Ph.D. Dissertation, Western Michigan University (2010).

Allan Bickle, Collapsible graphs, Congr. Numer. 231 (2018), 165-172.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

a(n) = ceiling(2*n/5) = A057354(n) for n > 7.

G.f.: x^4*(4 - 4*x^5 + x^7 + x^9)/((x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - Stefano Spezia, Feb 05 2022

Example

For n between 4 and 6, 3-collapsible graphs with 4 degree 3 vertices are:
- a complete graph with 4 vertices,
- a wheel with 5 vertices,
- the graph formed by removing a 4-cycle and a 2-clique from a complete graph with 6 vertices.

Mathematica

A350716[n_]:=If[n<8, 4, Ceiling[2n/5]];
Array[A350716, 100, 4] (* Paolo Xausa, Dec 01 2023 *)

Prog

(Python)
print([4, 4, 4, 4] + [2*n//5 for n in range(10, 80)]) # Gennady Eremin, Feb 05 2022

Crossrefs

Cf. A351169, A057354.

Sequence in context: A096300 A333534 A035672 * A113472 A105682 A049109

Adjacent sequences: A350713 A350714 A350715 * A350717 A350718 A350719

Keyword

nonn,easy

Author

Allan Bickle, Feb 03 2022

Status

approved