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

%I A350716 #29 Dec 01 2023 05:22:16
%S A350716 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,
%T A350716 14,14,14,15,15,16,16,16,17,17,18,18,18,19,19,20,20,20,21,21,22,22,22,
%U A350716 23,23,24,24,24,25,25,26,26,26,27,27,28,28,28,29,29,30
%N A350716 a(n) is the minimum number of vertices of degree 3 over all 3-collapsible graphs with n vertices.
%C A350716 A graph G is k-collapsible if it has minimum degree k and has no proper induced subgraph with minimum degree k.
%H A350716 Paolo Xausa, <a href="/A350716/b350716.txt">Table of n, a(n) for n = 4..10000</a>
%H A350716 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 A350716 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/collapsiblepaper.pdf">Collapsible graphs</a>, Congr. Numer. 231 (2018), 165-172.
%H A350716 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A350716 a(n) = ceiling(2*n/5) = A057354(n) for n > 7.
%F A350716 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
%e A350716 For n between 4 and 6, 3-collapsible graphs with 4 degree 3 vertices are:
%e A350716 - a complete graph with 4 vertices,
%e A350716 - a wheel with 5 vertices,
%e A350716 - the graph formed by removing a 4-cycle and a 2-clique from a complete graph with 6 vertices.
%t A350716 A350716[n_]:=If[n<8,4,Ceiling[2n/5]];
%t A350716 Array[A350716,100,4] (* _Paolo Xausa_, Dec 01 2023 *)
%o A350716 (Python)
%o A350716 print([4,4,4,4] + [2*n//5 for n in range(10, 80)]) # _Gennady Eremin_, Feb 05 2022
%Y A350716 Cf. A351169, A057354.
%K A350716 nonn,easy
%O A350716 4,1
%A A350716 _Allan Bickle_, Feb 03 2022