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dual_decomposition: extend strengthened conjecture table to n=20

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n=19 (21,138 col., 68s) and n=20 (107,874 col., 361s) both pass.
New total for clauses (1)-(4) over n<=20: 142,812/142,812.

Also bump max_n in check_conj_3_8_scaled.py default to 20 (was 18) and
time_budget_per_n to 7200s.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-24 14:16:10 -04:00
parent 83e9dba8ac
commit b6f2ee8d6e
5 changed files with 11 additions and 9 deletions
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papers/dual_decomposition_minimal_counterexamples/experiments/check_conj_3_8_scaled.py
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@@ -359,7 +359,7 @@ def check_clause_4_kempe_part(H, edges, col_list, named, witness, a, b, c,
return count == 1
def main(max_n=18, time_budget_per_n=3600):
def main(max_n=20, time_budget_per_n=7200):
rows = []
for n in range(12, max_n + 1):
start = time.time()
papers/dual_decomposition_minimal_counterexamples/paper.aux
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@@ -26,10 +26,10 @@
\newlabel{rem:conj-3-6-empirical}{{4.2}{9}}
\newlabel{conj:face-monochromatic-pair-strengthened}{{4.3}{10}}
\newlabel{rem:conj-3-8-empirical}{{4.4}{10}}
\newlabel{rem:implication-4ct}{{4.5}{10}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{0pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\newlabel{rem:implication-4ct}{{4.5}{11}}
\gdef \@abspage@last{11}
papers/dual_decomposition_minimal_counterexamples/paper.log
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This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 24 MAY 2026 14:15
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -303,7 +303,7 @@ b></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb
/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb></
usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pf
b>
Output written on paper.pdf (11 pages, 941151 bytes).
Output written on paper.pdf (11 pages, 941265 bytes).
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papers/dual_decomposition_minimal_counterexamples/paper.pdf
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papers/dual_decomposition_minimal_counterexamples/paper.tex
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@@ -647,12 +647,14 @@ $(F, e_1, e_2)$ whose accompanying $f_n$ satisfies clause~(4) (see
\begin{tabular}{r|r|r|r|l}
$n$ & \#tri & \#col.\ tested & \#sat. & status \\
\hline
$14$ & $1$ & $216$ & $216$ & all pass \\
$16$ & $3$ & $864$ & $864$ & all pass \\
$17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\
$18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\
$14$ & $1$ & $216$ & $216$ & all pass \\
$16$ & $3$ & $864$ & $864$ & all pass \\
$17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\
$18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\
$19$ & $23$ & $21{,}138$ & $21{,}138$ & all pass \\
$20$ & $73$ & $107{,}874$ & $107{,}874$ & all pass \\
\hline
total ($n \le 18$) & $20$ & $13{,}800$ & $13{,}800$ & \\
total ($n \le 20$) & $116$ & $142{,}812$ & $142{,}812$ & \\
\end{tabular}
\end{center}
\noindent A subtlety: only about half of the