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

KEYWORD

nonn,easy

AUTHOR

Allan Bickle, Feb 03 2022

STATUS

approved