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A351169 a(n) is the minimum number of vertices of degree 4 over all 4-collapsible graphs with n vertices.

%I A351169 #36 Nov 30 2023 16:22:51
%S A351169 5,4,3,3,3,3,4,4,4,4,5,5,5,6,6,6,6,7,7,7,8,8,8,8,9,9,9,10,10,10,10,11,
%T A351169 11,11,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16,16,16,16,17,17,17,
%U A351169 18,18,18,18,19,19,19,20,20,20,20,21,21,21,22,22,22
%N A351169 a(n) is the minimum number of vertices of degree 4 over all 4-collapsible graphs with n vertices.
%C A351169 A graph G is k-collapsible if it has minimum degree k and has no proper induced subgraph with minimum degree k.
%H A351169 Gennady Eremin, <a href="/A351169/b351169.txt">Table of n, a(n) for n = 5..10000</a>
%H A351169 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/dissertation4.pdf">The k-Cores of a Graph</a>, Ph.D. Dissertation, Western Michigan University (2010).
%H A351169 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/collapsiblepaper.pdf">Collapsible graphs</a>, Congr. Numer. 231 (2018), 165-172.
%H A351169 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A351169 a(n) = ceiling(2*n/7) for n > 7.
%F A351169 G.f.: x^5*(5 - x - x^2 + x^6 - 5*x^7 + x^8 + x^9 + x^10)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - _Stefano Spezia_, Feb 05 2022
%e A351169 A complete graph with 5 vertices is 4-collapsible with 5 degree 4 vertices.
%e A351169 The graph formed by removing two nonadjacent edges from a complete graph with 6 vertices is 4-collapsible with 4 degree 4 vertices.
%t A351169 A351169[n_]:=If[n<8,10-n,Ceiling[2n/7]];
%t A351169 Array[A351169,100,5] (* _Paolo Xausa_, Nov 30 2023 *)
%o A351169 (Python)
%o A351169 print([5,4,3] + [1+(2*n-1)//7 for n in range(8, 80)]) # _Gennady Eremin_, Mar 07 2022
%o A351169 (PARI) a(n) = if(n<8,10-n,(2*n+6)\7); \\ _Kevin Ryde_, Mar 08 2022
%Y A351169 Cf. A350716, A057356.
%K A351169 nonn,easy
%O A351169 5,1
%A A351169 _Allan Bickle_, Feb 03 2022