The On-Line Encyclopedia of Integer Sequences (OEIS)

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A006855

Maximum number of edges in an n-node squarefree graph, or, in a graph containing no 4-cycle, or no C_4.
(history; published version)

#76 by Andrew Howroyd at Thu Aug 15 10:58:21 EDT 2024

STATUS

reviewed

approved

#75 by Michel Marcus at Thu Aug 15 10:41:10 EDT 2024

STATUS

proposed

reviewed

#74 by Pontus von Brömssen at Thu Aug 15 10:35:26 EDT 2024

STATUS

editing

proposed

#73 by Pontus von Brömssen at Thu Aug 15 10:34:52 EDT 2024

LINKS

Zoltan Zoltán Füredi, <a href="http://www.math.uiuc.edu/~z-furedi/PUBS/furedi_C4abs.pdf">Quadrilateral-free graphs with maximum number of edges</a>, Extended abstract, Proceedings of the Japan Workshop on Graph Th. and Combinatorics, University, Yokohama, Japan 1994, pp. 13-22 (see Section 6).

Zoltan Zoltán Füredi, <a href="https://doi.org/10.1006/jctb.1996.0052">On the number of edges of quadrilateral-free graphs</a>, J. Combin. Theory (B) 68 (1996), 1-6.

STATUS

approved

editing

#72 by Peter Luschny at Tue Mar 14 03:50:31 EDT 2023

STATUS

reviewed

approved

#71 by Joerg Arndt at Tue Mar 14 03:40:51 EDT 2023

STATUS

proposed

reviewed

#70 by Jon E. Schoenfield at Tue Mar 14 01:00:51 EDT 2023

STATUS

editing

proposed

#69 by Jon E. Schoenfield at Tue Mar 14 00:59:45 EDT 2023

COMMENTS

From _Lower bounds that have a good chance of being exact: a(41) >= 132, a(42) >= 137, a(43) >= 142, a(44) >= 148, a(45) >= 154, a(46) >= 157, a(47) >= 163, a(48) >= 168, a(49) >= 174. - _Brendan McKay_, Mar 08 2022: (Start)

Lower bounds that have a good chance of being exact:

a(41)>=132, a(42)>=137, a(43)>=142, a(44)>=148, a(45)>=154,

a(46)>=157, a(47)>=163, a(48)>=168, a(49)>=174. (End)

STATUS

proposed

editing

#68 by Max Alekseyev at Mon Mar 13 17:48:12 EDT 2023

STATUS

editing

proposed

#67 by Max Alekseyev at Mon Mar 13 17:47:51 EDT 2023

DATA

0, 1, 3, 4, 6, 7, 9, 11, 13, 16, 18, 21, 24, 27, 30, 33, 36, 39, 42, 46, 50, 52, 56, 59, 63, 67, 71, 76, 80, 85, 90, 92, 96, 102, 106, 110, 113, 117, 122, 127

COMMENTS

a(40)>=127, a(41)>=132, a(42)>=137, a(43)>=142, a(44)>=148, a(45)>=154,

Upper bounds: a(40) <= 128, a(41) <= 134, 133, a(42) <= 140, 139, a(43) <= 146, 145, a(44) <= 152, 151, a(45) <= 159, 158, a(46) <= 166, 165, a(47) <= 173, 171, a(48) <= 180, 176, a(49) <= 187182. - Max Alekseyev, Jan 26 2023

LINKS

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

EXTENSIONS

a(40) from Brendan McKay, communicated by Max Alekseyev, Mar 13 2023

STATUS

approved

editing