A350292 - OEIS

%I #10 Dec 25 2021 14:54:23

%S 1,2,1,6,3,1,12,8,4,1,24,20,10,5,1

%N Triangle read by rows: the n-th row gives the saturated vertex Turán numbers for the cube graph Q_n.

%C The k-th saturated vertex Turán number for the cube graph Q_n is the maximum number of vertices to be deleted from the cube graph such that no subgraph Q_k is complete and each of the deleted vertices being added again completes a subgraph Q_k (see Harborth and Nienborg).

%H Heiko Harborth and Hauke Nienborg, <a href="https://www.researchgate.net/publication/266861957_Saturated_vertex_Turan_numbers_for_cube_graphs">Saturated vertex Turán numbers for cube graphs</a>, Congr. Num. 208 (2011), 183-188.

%H Mathonline, <a href="http://mathonline.wikidot.com/cube-graphs">Cube Graphs</a>

%F T(n, n) = 1 and T(n, n-1) = n (see Theorem 2 in Harborth and Nienborg).

%e n\k |   1    2    3    4    5

%e ----+------------------------

%e   1 |   1

%e   2 |   2    1

%e   3 |   6    3    1

%e   4 |  12    8    4    1

%e   5 |  24   20   10    5    1

%e   ...

%Y Cf. A350293 (k = 1), A350295 (2nd subdiagonal).

%K nonn,tabl,more

%O 1,2

%A _Stefano Spezia_, Dec 23 2021