#13546: Bug in is_perfect
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Reporter: azi | Owner: jason, ncohen, rlm
Type: defect | Status: new
Priority: critical | Milestone: sage-5.5
Component: graph theory | Keywords: is_perfect,graph theory
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Jernej Azarija
Merged in: | Dependencies:
Stopgaps: |
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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).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13546>
Sage <http://www.sagemath.org>
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