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

Add connected tire clusters with two-cluster-per-vertex proposition

Browse Source 
Define a connected tire cluster (union of same-depth tires joined by
shared vertices, transitive closure), prove same-depth tires meet only
in vertices, and prove every vertex lies in at most two clusters (one at
each of two consecutive depths) -- the bounded coarsening of the
unbounded per-vertex tire count.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-06-17 01:03:37 -04:00
parent 251c453437
commit 646cf9d12f
4 changed files with 154 additions and 40 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/heawood_restrictions_on_nested_tire_graph_duals/paper.log
+31 -27
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) 17 JUN 2026 00:42
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 17 JUN 2026 01:03
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -192,35 +192,39 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
e
))
[1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
[2] [3] (./paper.aux) )
[2] [3] [4] (./paper.aux) )
Here is how much of TeX's memory you used:
3002 strings out of 478268
41895 string characters out of 5846347
340223 words of memory out of 5000000
21051 multiletter control sequences out of 15000+600000
475975 words of font info for 54 fonts, out of 8000000 for 9000
3012 strings out of 478268
42080 string characters out of 5846347
342271 words of memory out of 5000000
21059 multiletter control sequences out of 15000+600000
476880 words of font info for 57 fonts, out of 8000000 for 9000
1302 hyphenation exceptions out of 8191
69i,7n,76p,242b,278s 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/cmbx8.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/cmr10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/
cmr5.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr
7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.p
fb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pf
b></usr/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/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></u
sr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb>
Output written on paper.pdf (3 pages, 210205 bytes).
69i,7n,76p,242b,264s stack positions out of 10000i,1000n,20000p,200000b,200000s
</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/cmbx8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/
amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/
amsfonts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/a
msfonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/am
sfonts/cm/cmmi5.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/cmr5.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/cm
r8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmss1
0.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10
.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy5.p
fb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.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/symbols/msam10.pf
b></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm1
0.pfb>
Output written on paper.pdf (4 pages, 241965 bytes).
PDF statistics:
94 PDF objects out of 1000 (max. 8388607)
56 compressed objects within 1 object stream
112 PDF objects out of 1000 (max. 8388607)
67 compressed objects within 1 object stream
0 named destinations out of 1000 (max. 500000)
1 words of extra memory for PDF output out of 10000 (max. 10000000)