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A205805 Maximum number of edges in a squarefree bipartite graph on n vertices. 5

%I #27 Mar 15 2023 11:40:05

%S 0,1,2,3,4,6,7,9,10,12,14,16,18,21,22,24,26,29,31,34,36,39,42,45,48,

%T 52,53,56,58,61,64,67,70,74,77,81,84,88,92,96,100,105,106,108,110,115,

%U 118,122,126,130,134,138,142,147,151,156,160,165,170,175,180,186,187

%N Maximum number of edges in a squarefree bipartite graph on n vertices.

%C Zarankiewicz number z(n; C_4).

%C The corresponding extremal graphs for n in {1, 2, 6, 14, 26, 28, 42, 46, 62} are regular and unique. The extremal graphs for n = 16 consist of a regular graph and three other graphs. - _Max Alekseyev_, Mar 14 2023

%H Wayne Goddard, Michael A. Henning, and Ortrud R. Oellermann, <a href="https://doi.org/10.1016/S0012-365X(99)00370-2">Bipartite Ramsey numbers and Zarankiewicz numbers</a>, Discrete Math. 219 (2000), no. 1-3, 85-95.

%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/extremal.html">Extremal Graphs and Turan numbers</a>.

%F For n > 2, a(n) <= floor( a(n-1)*n/(n-2) ). - _Max Alekseyev_, Mar 09 2023

%Y Cf. A006855.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jan 31 2012

%E a(21)-a(45) from _Max Alekseyev_, Mar 13 2023

%E a(46)-a(63) from _Brendan McKay_, communicated by _Max Alekseyev_, Mar 14 2023

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