dual_decomposition: 4-edge-face criterion, Conj 3.8, cubic contraction theorem
- Conjecture 3.6: add the 4-edge-face criterion as clause (3), with empirical table through n=21 (complete, 535,182/535,182 pass) plus partial n=22 (641,700 colourings, timed out). - Conjecture 3.8: strengthening with clause (4) on the b,c-Kempe cycle / 3-colour alternative on the new face f_n; existential at the witness level. Tested through n=18 (13,800/13,800 pass). - Definition + figure for cubic-graph edge contraction (delete edge, smooth the resulting degree-2 endpoints; equivalent to simple contraction in the dual). - Theorem: cubic contraction across a 4-face preserves 3-edge-colourability when the two opposite boundary edges have different colours. Constructive proof: the two smoothed-in edges inherit the colour of the w_i pair they absorb, and e_1 is recoloured to the third colour. - Add 2-panel illustration of the theorem's recolouring. - Trim Remark 3.7 and 3.9 tables to fit within \textwidth. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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44739 string characters out of 5846347
|
||||
347356 words of memory out of 5000000
|
||||
21143 multiletter control sequences out of 15000+600000
|
||||
478077 words of font info for 62 fonts, out of 8000000 for 9000
|
||||
1302 hyphenation exceptions out of 8191
|
||||
69i,9n,76p,1306b,398s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||
</usr/local/texlive/2022/texmf-dist/fonts/type1/public/ams
|
||||
fonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsf
|
||||
onts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsf
|
||||
onts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfo
|
||||
nts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfon
|
||||
ts/cm/cmmi5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts
|
||||
/cm/cmmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/c
|
||||
m/cmmi9.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/
|
||||
cmr10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cm
|
||||
r5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.
|
||||
pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb
|
||||
></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb></
|
||||
usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></u
|
||||
sr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy5.pfb></usr
|
||||
/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/l
|
||||
ocal/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy9.pfb></usr/loc
|
||||
al/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/loca
|
||||
l/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/
|
||||
texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb></usr/local/t
|
||||
exlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
|
||||
Output written on paper.pdf (13 pages, 1144897 bytes).
|
||||
PDF statistics:
|
||||
172 PDF objects out of 1000 (max. 8388607)
|
||||
92 compressed objects within 1 object stream
|
||||
0 named destinations out of 1000 (max. 500000)
|
||||
61 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||
|
||||
|
||||
Reference in New Issue
Block a user