#13546: Bug in is_perfect
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Reporter: azi | Owner: jason, ncohen, rlm
Type: defect | Status: positive_review
Priority: critical | Milestone: sage-5.7
Component: graph theory | Resolution:
Keywords: is_perfect,graph theory | Work issues:
Report Upstream: N/A | Reviewers: Jernej Azarija,
Sébastien Labbé
Authors: Nathann Cohen | Merged in:
Dependencies: #8952 | Stopgaps:
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Changes (by ncohen):
* status: needs_work => positive_review
Old description:
> The method for recognizing perfect graphs if flawed. Consider the
> following sage function:
> {{{
> def f(n):
> c= 0
> for g in graphs.nauty_geng(str(n)):
> if g.is_perfect():
> c+=1
> return c
>
> }}}
>
> one can readily see that f(7) = 607 and f(8) = 8899 which is, (according
> to oeis http://oeis.org/A052431) incorrect. What should be true is that
> f(7) = 906 and f(7) = 8887.
>
> I propose to rewrite a correct algorithm perhaps using the polynomial
> algorithm (www.comp.leeds.ac.uk/vuskovi/FOCS03final.ps).
New description:
The method for recognizing perfect graphs if flawed. Consider the
following sage function:
{{{
def f(n):
c= 0
for g in graphs.nauty_geng(str(n)):
if g.is_perfect():
c+=1
return c
}}}
one can readily see that f(7) = 607 and f(8) = 8899 which is, (according
to oeis http://oeis.org/A052431) incorrect. What should be true is that
f(7) = 906 and f(7) = 8887.
I propose to rewrite a correct algorithm perhaps using the polynomial
algorithm (www.comp.leeds.ac.uk/vuskovi/FOCS03final.ps).
Apply :
* [attachment:trac_13546.2.patch]
--
Comment:
Good to go ! I had to ask David to check it on his computer as Sage
segfaults on mine on exit, which prevents me from running tests `:-/`
Nathann
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13546#comment:37>
Sage <http://www.sagemath.org>
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