[seqfan] Re: Max no. of edges in graph with no 4-cycles

[Neil Sloane]

Hi Brendan!  Thanks for those additional terms.
I think people would find it helpful to see the lower bounds for 40 to 49
-  could you add them in the COMMENTS section?

I see you also extended A335830, which gives the number of optimal graphs.

Are the actual graphs available anywhere on your web site?

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com



On Tue, Mar 8, 2022 at 3:21 AM Brendan McKay via SeqFan <
seqfan at list.seqfan.eu> wrote:

> I added a(32)-a(39) to A006855, namely 92,96,102,106,110,113,117,122.
>
> I also have lower bounds for a(40)-a(49) that are probably exact, but
> I didn't prove them.
>
> Brendan.
>
> On 8/3/2022 4:36 am, Neil Sloane wrote:
> > PS Allan Wechsler kindly pointed me to A006855.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email:njasloane at gmail.com
> >
> >
> >
> > On Mon, Mar 7, 2022 at 11:45 AM Neil Sloane<njasloane at gmail.com>  wrote:
> >
> >> Let b(n) be the maximum number of edges in a graph on n nodes that
> >> contains no 4-cycle.
> >>
> >> It seems to start (for n>=1) 0, 1, 3, 4, 7, 9?
> >>
> >> Is it missing from the OEIS?
> >>
> >>
> >> This question came up because M S Smith seems to have proved that b(n)
> is
> >> an upper bound on Stan Wagon's Problem of the Week #1321 (and also on
> >> A347301). Happy to send anyone who is interested a copy of Smith's
> email.
> >>
> >>
> >> Best regards
> >> Neil
> >>
> >> Neil J. A. Sloane, Chairman, OEIS Foundation.
> >> Also Visiting Scientist, Math. Dept., Rutgers University,
> >> Email:njasloane at gmail.com
> >>
> >>
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