login
A350716
a(n) is the minimum number of vertices of degree 3 over all 3-collapsible graphs with n vertices.
2
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
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.
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
Sequence in context: A333534 A372512 A035672 * A113472 A105682 A049109
KEYWORD
nonn,easy
AUTHOR
Allan Bickle, Feb 03 2022
STATUS
approved