A006856 - OEIS

%I M0624 #60 Jan 06 2023 10:55:03

%S 0,1,2,3,5,6,8,10,12,15,16,18,21,23,26,28,31,34,38,41,44,47,50,54,57,

%T 61,65,68,72,76,80,85,87,90,95,99,104,109,114,120,124,129,134,139,145,

%U 150,156,162,168,175,176,178,181

%N Maximal number of edges in n-node graph of girth at least 5.

%C From _Brendan McKay_, Mar 09 2022: (Start)

%C The unique graph for a(50)=175 is the Hoffman-Singleton graph.

%C a(53) is at least 181. (End)

%C a(53) is exactly 181. a(54)-a(56) are at least 185,189,193. - _Brendan McKay_, Jan 07 2023

%D Brendan McKay, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. Backelin, <a href="http://arxiv.org/abs/1511.08128">Sizes of the extremal girth 5 graphs of orders from 40 to 49</a>, arXiv preprint arXiv:1511.08128 [math.CO], 2015.

%H Michael Codish, Alice Miller, Patrick Prosser, and Peter J. Stuckey, <a href="http://www.cs.bgu.ac.il/~mcodish/Papers/Pages/ijcai2013.html">Breaking Symmetries in Graph Representation</a>, IJCAI 2013.

%H David K. Garnick, Y. H. Harris Kwong and Felix Lazebnik, <a href="http://www.math.udel.edu/~lazebnik/papers/ex34a_v2.pdf">Extremal Graphs without Three-Cycles or Four-Cycles</a>, Journal of Graph Theory, 17 (1993), 633-645.

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

%H Alice Miller and Michael Codish, <a href="https://arxiv.org/abs/1708.06576">Graphs with girth at least 5 with orders between 20 and 32</a>, arXiv:1708.06576 [math.CO], 2017.

%Y Cf. A159847.

%K nonn,more

%O 1,3

%A _N. J. A. Sloane_

%E Two more terms from David Garnick (dgarnick(AT)gmail.com), Jan 09 2007

%E Two more terms from _Michael Codish_, Apr 07 2013

%E Definition clarified by _Jörgen Backelin_, Jun 18 2015

%E a(33)-a(52) from _Brendan McKay_, Mar 09 2022

%E a(53) from _Brendan McKay_, Jan 06 2023