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
Examples
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.
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).
Programs
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Mathematica
A350716[n_]:=If[n<8,4,Ceiling[2n/5]]; Array[A350716,100,4] (* Paolo Xausa, Dec 01 2023 *)
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Python
print([4,4,4,4] + [2*n//5 for n in range(10, 80)]) # Gennady Eremin, Feb 05 2022
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
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