didericis/math-research
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Frame flip-asymmetry as first of further necessary properties

Browse Source 
Adds a transitional section reframing the frequency results: the
relevant class is not all maximal planar graphs but those that resist
Kempe-style reductions, where flip-asymmetry's exclusion may have
real bite. Sets up subsequent development of additional necessary
properties of a minimum-order 5-chromatic counterexample.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-14 00:18:34 -04:00
parent 076137baaa
commit bd409585ba
5 changed files with 36 additions and 22 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/flip_symmetric_maximal_planar_graphs/paper.log
+18 -18
View File
@@ -1,4 +1,4 @@
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 14 MAY 2026 00:12
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 14 MAY 2026 00:17
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -502,7 +502,7 @@ hs \OT1/cmr/m/n/10 with \OT1/cmtt/m/n/10 minimum[]connectivity $\OT1/cmr/m/n/10
=
[]
[2] [3] (./paper.aux) )
[2] [3] [4] (./paper.aux) )
Here is how much of TeX's memory you used:
13153 strings out of 478268
265523 string characters out of 5846347
@@ -511,23 +511,23 @@ Here is how much of TeX's memory you used:
475834 words of font info for 54 fonts, out of 8000000 for 9000
1302 hyphenation exceptions out of 8191
100i,8n,104p,386b,794s stack positions out of 10000i,1000n,20000p,200000b,200000s
</usr/local/texlive/2022/texmf-dist/fonts/type1/public/a
msfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/am
sfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/am
sfonts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/ams
fonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsf
onts/cm/cmmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfon
ts/cm/cmr10.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/cm
sy10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmt
i10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti
8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10
.pfb>
Output written on paper.pdf (3 pages, 164862 bytes).
</usr/local/texlive/2022/texmf-dist/fonts/type1/publ
ic/amsfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/publi
c/amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/publi
c/amsfonts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public
/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/
amsfonts/cm/cmmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/am
sfonts/cm/cmr10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsf
onts/cm/cmr7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfont
s/cm/cmr8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/c
m/cmsy10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm
/cmti10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/
cmti8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cm
tt10.pfb>
Output written on paper.pdf (4 pages, 165847 bytes).
PDF statistics:
77 PDF objects out of 1000 (max. 8388607)
47 compressed objects within 1 object stream
80 PDF objects out of 1000 (max. 8388607)
49 compressed objects within 1 object stream
0 named destinations out of 1000 (max. 500000)
13 words of extra memory for PDF output out of 10000 (max. 10000000)