Scaffold Heawood restrictions on nested tire graph duals paper
Add a new paper stub referencing the nested tire decompositions paper, with intro, Heawood bibliography entry, and an empty restrictions section. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
@@ -0,0 +1,21 @@
|
||||
\relax
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\citation{bauerfeld-nested-tires}
|
||||
\bibcite{Heawood1898}{1}
|
||||
\bibcite{bauerfeld-depth}{2}
|
||||
\bibcite{bauerfeld-nested-tires}{3}
|
||||
\bibcite{bauerfeld-nested-tire-duals}{4}
|
||||
\newlabel{tocindent-1}{0pt}
|
||||
\newlabel{tocindent0}{12.7778pt}
|
||||
\newlabel{tocindent1}{17.77782pt}
|
||||
\newlabel{tocindent2}{0pt}
|
||||
\newlabel{tocindent3}{0pt}
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Heawood restrictions on the tire dual}}{1}{}\protected@file@percent }
|
||||
\newlabel{sec:heawood-restrictions}{{2}{1}}
|
||||
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{1}{}\protected@file@percent }
|
||||
\gdef \@abspage@last{1}
|
||||
@@ -0,0 +1,64 @@
|
||||
# Fdb version 3
|
||||
["pdflatex"] 1781668577 "paper.tex" "paper.pdf" "paper" 1781668578
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1246382020 916 f87d7c45f9c908e672703b83b72241a3 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm" 1246382020 924 9904cf1d39e9767e7a3622f2a125a565 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1246382020 928 2dc8d444221b7a635bb58038579b861a ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1246382020 908 2921f8a10601f252058503cc6570e581 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm" 1246382020 940 75ac932a52f80982a9f8ea75d03a34cf ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1246382020 940 228d6584342e91276bf566bcf9716b83 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1136768653 1328 c834bbb027764024c09d3d2bf908b5f0 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmbx8.tfm" 1136768653 1332 1fde11373e221473104d6cc5993f046e ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmcsc10.tfm" 1136768653 1300 63a6111ee6274895728663cf4b4e7e81 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1136768653 1512 f21f83efb36853c0b70002322c1ab3ad ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1136768653 1520 eccf95517727cb11801f4f1aee3a21b4 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1136768653 1300 b62933e007d01cfd073f79b963c01526 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1136768653 1292 21c1c5bfeaebccffdb478fd231a0997d ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti10.tfm" 1136768653 1480 aa8e34af0eb6a2941b776984cf1dfdc4 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/cm/cmti8.tfm" 1136768653 1504 1747189e0441d1c18f3ea56fafc1c480 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1248133631 34811 78b52f49e893bcba91bd7581cdc144c0 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx8.pfb" 1248133631 32166 b0c356b15f19587482a9217ce1d8fa67 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb" 1248133631 32001 6aeea3afe875097b1eb0da29acd61e28 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb" 1248133631 36281 c355509802a035cadc5f15869451dcee ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1248133631 32762 224316ccc9ad3ca0423a14971cfa7fc1 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1248133631 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1248133631 32716 08e384dc442464e7285e891af9f45947 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb" 1248133631 37944 359e864bd06cde3b1cf57bb20757fb06 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb" 1248133631 35660 fb24af7afbadb71801619f1415838111 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls" 1591045760 61881 a7369c346c2922a758ae6283cc1ed014 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1359763108 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1359763108 13829 94730e64147574077f8ecfea9bb69af4 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd" 1359763108 961 6518c6525a34feb5e8250ffa91731cff ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd" 1359763108 961 d02606146ba5601b5645f987c92e6193 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1622667781 2222 da905dc1db75412efd2d8f67739f0596 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty" 1622667781 4173 bc0410bcccdff806d6132d3c1ef35481 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty" 1636758526 87648 07fbb6e9169e00cb2a2f40b31b2dbf3c ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty" 1636758526 4128 8eea906621b6639f7ba476a472036bbe ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty" 1636758526 2444 926f379cc60fcf0c6e3fee2223b4370d ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1465944070 1224 978390e9c2234eab29404bc21b268d1e ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def" 1601931164 19103 48d29b6e2a64cb717117ef65f107b404 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty" 1622581934 18399 7e40f80366dffb22c0e7b70517db5cb4 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty" 1636758526 7996 a8fb260d598dcaf305a7ae7b9c3e3229 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty" 1622581934 2671 4de6781a30211fe0ea4c672e4a2a8166 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty" 1636758526 4009 187ea2dc3194cd5a76cd99a8d7a6c4d0 ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def" 1644269979 29921 d0acc05a38bd4aa3af2017f0b7c137ce ""
|
||||
"/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1279039959 678 4792914a8f45be57bb98413425e4c7af ""
|
||||
"/usr/local/texlive/2022/texmf-dist/web2c/texmf.cnf" 1646502317 40171 cdab547de63d26590bebb3baff566530 ""
|
||||
"/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1647878959 4410336 7d30a02e9fa9a16d7d1f8d037ba69641 ""
|
||||
"/usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt" 1665017617 2826443 7e98410c533054b636c6470db83a27bc ""
|
||||
"/usr/local/texlive/2022/texmf.cnf" 1647878952 577 209b46be99c9075fd74d4c0369380e8c ""
|
||||
"paper.aux" 1781668577 894 c07070c22299dc3a5b11f2d70e9e6864 "pdflatex"
|
||||
"paper.tex" 1781668572 3984 c8e5ad80c1dfc803df154b6857fc59b0 ""
|
||||
(generated)
|
||||
"paper.aux"
|
||||
"paper.log"
|
||||
"paper.pdf"
|
||||
@@ -0,0 +1,222 @@
|
||||
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 17 JUN 2026 00:31
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
%&-line parsing enabled.
|
||||
**paper.tex
|
||||
(./paper.tex
|
||||
LaTeX2e <2021-11-15> patch level 1
|
||||
L3 programming layer <2022-02-24>
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
|
||||
Document Class: amsart 2020/05/29 v2.20.6
|
||||
\linespacing=\dimen138
|
||||
\normalparindent=\dimen139
|
||||
\normaltopskip=\skip47
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2021/10/15 v2.17l AMS math features
|
||||
\@mathmargin=\skip48
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2021/08/26 v2.01 AMS text
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks16
|
||||
\ex@=\dimen140
|
||||
))
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen141
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 2021/08/26 v2.02 operator names
|
||||
)
|
||||
\inf@bad=\count185
|
||||
LaTeX Info: Redefining \frac on input line 234.
|
||||
\uproot@=\count186
|
||||
\leftroot@=\count187
|
||||
LaTeX Info: Redefining \overline on input line 399.
|
||||
\classnum@=\count188
|
||||
\DOTSCASE@=\count189
|
||||
LaTeX Info: Redefining \ldots on input line 496.
|
||||
LaTeX Info: Redefining \dots on input line 499.
|
||||
LaTeX Info: Redefining \cdots on input line 620.
|
||||
\Mathstrutbox@=\box50
|
||||
\strutbox@=\box51
|
||||
\big@size=\dimen142
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
||||
\macc@depth=\count190
|
||||
\c@MaxMatrixCols=\count191
|
||||
\dotsspace@=\muskip16
|
||||
\c@parentequation=\count192
|
||||
\dspbrk@lvl=\count193
|
||||
\tag@help=\toks17
|
||||
\row@=\count194
|
||||
\column@=\count195
|
||||
\maxfields@=\count196
|
||||
\andhelp@=\toks18
|
||||
\eqnshift@=\dimen143
|
||||
\alignsep@=\dimen144
|
||||
\tagshift@=\dimen145
|
||||
\tagwidth@=\dimen146
|
||||
\totwidth@=\dimen147
|
||||
\lineht@=\dimen148
|
||||
\@envbody=\toks19
|
||||
\multlinegap=\skip49
|
||||
\multlinetaggap=\skip50
|
||||
\mathdisplay@stack=\toks20
|
||||
LaTeX Info: Redefining \[ on input line 2938.
|
||||
LaTeX Info: Redefining \] on input line 2939.
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 397
|
||||
.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
||||
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||
\symAMSa=\mathgroup4
|
||||
\symAMSb=\mathgroup5
|
||||
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||
)
|
||||
\copyins=\insert199
|
||||
\abstractbox=\box52
|
||||
\listisep=\skip51
|
||||
\c@part=\count197
|
||||
\c@section=\count198
|
||||
\c@subsection=\count266
|
||||
\c@subsubsection=\count267
|
||||
\c@paragraph=\count268
|
||||
\c@subparagraph=\count269
|
||||
\c@figure=\count270
|
||||
\c@table=\count271
|
||||
\abovecaptionskip=\skip52
|
||||
\belowcaptionskip=\skip53
|
||||
\captionindent=\dimen149
|
||||
\thm@style=\toks21
|
||||
\thm@bodyfont=\toks22
|
||||
\thm@headfont=\toks23
|
||||
\thm@notefont=\toks24
|
||||
\thm@headpunct=\toks25
|
||||
\thm@preskip=\skip54
|
||||
\thm@postskip=\skip55
|
||||
\thm@headsep=\skip56
|
||||
\dth@everypar=\toks26
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphicx.sty
|
||||
Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/keyval.sty
|
||||
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
|
||||
\KV@toks@=\toks27
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/graphics.sty
|
||||
Package: graphics 2021/03/04 v1.4d Standard LaTeX Graphics (DPC,SPQR)
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics/trig.sty
|
||||
Package: trig 2021/08/11 v1.11 sin cos tan (DPC)
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
|
||||
File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
|
||||
)
|
||||
Package graphics Info: Driver file: pdftex.def on input line 107.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/graphics-def/pdftex.def
|
||||
File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex
|
||||
))
|
||||
\Gin@req@height=\dimen150
|
||||
\Gin@req@width=\dimen151
|
||||
)
|
||||
\c@theorem=\count272
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
|
||||
File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count273
|
||||
\l__pdf_internal_box=\box53
|
||||
)
|
||||
(./paper.aux)
|
||||
\openout1 = `paper.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 27.
|
||||
LaTeX Font Info: ... okay on input line 27.
|
||||
LaTeX Font Info: Trying to load font information for U+msa on input line 27.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsa.fd
|
||||
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for U+msb on input line 27.
|
||||
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/amsfonts/umsb.fd
|
||||
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
||||
)
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
|
||||
[Loading MPS to PDF converter (version 2006.09.02).]
|
||||
\scratchcounter=\count274
|
||||
\scratchdimen=\dimen152
|
||||
\scratchbox=\box54
|
||||
\nofMPsegments=\count275
|
||||
\nofMParguments=\count276
|
||||
\everyMPshowfont=\toks28
|
||||
\MPscratchCnt=\count277
|
||||
\MPscratchDim=\dimen153
|
||||
\MPnumerator=\count278
|
||||
\makeMPintoPDFobject=\count279
|
||||
\everyMPtoPDFconversion=\toks29
|
||||
) (/usr/local/texlive/2022/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
|
||||
Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
|
||||
Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
|
||||
85.
|
||||
|
||||
(/usr/local/texlive/2022/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||
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}]
|
||||
(./paper.aux) )
|
||||
Here is how much of TeX's memory you used:
|
||||
2992 strings out of 478268
|
||||
41657 string characters out of 5846347
|
||||
336140 words of memory out of 5000000
|
||||
21041 multiletter control sequences out of 15000+600000
|
||||
475975 words of font info for 54 fonts, out of 8000000 for 9000
|
||||
1302 hyphenation exceptions out of 8191
|
||||
69i,5n,76p,242b,213s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||
</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/
|
||||
cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/c
|
||||
m/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/
|
||||
cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/c
|
||||
mmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr
|
||||
10.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/cmsy10.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 (1 page, 145461 bytes).
|
||||
PDF statistics:
|
||||
68 PDF objects out of 1000 (max. 8388607)
|
||||
40 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)
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,123 @@
|
||||
%% filename: amsart-template.tex
|
||||
%% American Mathematical Society
|
||||
%% AMS-LaTeX v.2 template for use with amsart
|
||||
%% ====================================================================
|
||||
|
||||
\documentclass{amsart}
|
||||
|
||||
\usepackage{amssymb}
|
||||
\usepackage{graphicx}
|
||||
|
||||
\newtheorem{theorem}{Theorem}[section]
|
||||
\newtheorem{lemma}[theorem]{Lemma}
|
||||
\newtheorem{corollary}[theorem]{Corollary}
|
||||
\newtheorem{proposition}[theorem]{Proposition}
|
||||
\newtheorem{conjecture}[theorem]{Conjecture}
|
||||
|
||||
\theoremstyle{definition}
|
||||
\newtheorem{definition}[theorem]{Definition}
|
||||
\newtheorem{example}[theorem]{Example}
|
||||
\newtheorem{xca}[theorem]{Exercise}
|
||||
|
||||
\theoremstyle{remark}
|
||||
\newtheorem{remark}[theorem]{Remark}
|
||||
|
||||
\numberwithin{equation}{section}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\title{Heawood Restrictions on Nested Tire Graph Duals}
|
||||
|
||||
% author one information
|
||||
\author{Eric Bauerfeld}
|
||||
\address{}
|
||||
\curraddr{}
|
||||
\email{}
|
||||
\thanks{}
|
||||
|
||||
\subjclass[2010]{Primary }
|
||||
|
||||
\keywords{plane graph, triangulation, plane depth, level edge, dual graph,
|
||||
tire graph, Heawood number}
|
||||
|
||||
\date{}
|
||||
|
||||
\dedicatory{}
|
||||
|
||||
\begin{abstract}
|
||||
%% TODO: abstract. Following \cite{bauerfeld-nested-tires}, which establishes
|
||||
%% the basic vocabulary of tire graphs and dual depth, we study the Heawood
|
||||
%% (mod-3 / face-sum) restrictions imposed on the duals of nested tire graphs.
|
||||
\end{abstract}
|
||||
|
||||
\maketitle
|
||||
|
||||
\section{Introduction}
|
||||
|
||||
A classical theorem of Tait recasts the Four Colour Theorem in dual,
|
||||
edge-colouring terms: a plane triangulation $G$ is properly $4$-vertex-colourable
|
||||
if and only if its dual cubic graph $G'$ is properly $3$-edge-colourable. Thus a
|
||||
minimal counterexample to the Four Colour Theorem -- a smallest triangulation
|
||||
admitting no proper $4$-colouring -- corresponds to a smallest cubic plane graph
|
||||
admitting no proper $3$-edge-colouring.
|
||||
|
||||
This paper continues the series studying that structure through the
|
||||
lens of \emph{nested level duals}. The foundational vocabulary ---
|
||||
level sources, levels, the inner planar dual $G'$ and its dual depth,
|
||||
and tire graphs --- is developed in the companion paper
|
||||
\cite{bauerfeld-nested-tires}; we refer to that paper for those
|
||||
definitions and rely on them throughout. In particular we use,
|
||||
without restating, the notions of:
|
||||
\begin{itemize}
|
||||
\item \emph{level source} $S$ and $G$-vertex levels $\ell_G(v)$;
|
||||
\item the inner planar dual $G'$
|
||||
(\cite[Definition~1.3]{bauerfeld-nested-tires});
|
||||
\item \emph{dual depth} $\delta_G(d_f)$
|
||||
(\cite[Definition~1.4]{bauerfeld-nested-tires});
|
||||
\item \emph{tire graph} $T = (B_{\mathrm{out}}, O, E_{\mathrm{ann}})$
|
||||
with outer/inner boundaries and annular edges
|
||||
(\cite[Definition~1.5]{bauerfeld-nested-tires});
|
||||
\item the \emph{tire-component lemma}
|
||||
(\cite[Lemma~1.8]{bauerfeld-nested-tires}); and
|
||||
\item the \emph{tire-tread partition theorem}
|
||||
(\cite[Theorem~1.9]{bauerfeld-nested-tires}).
|
||||
\end{itemize}
|
||||
|
||||
Throughout, $G = (V, E)$ is a plane maximal planar graph (a triangulation)
|
||||
with a fixed planar embedding $\Pi_G$. We write $|V| = n$, so $|E| = 3n - 6$
|
||||
and $G$ has $2n - 4$ triangular faces.
|
||||
|
||||
%% TODO: state the Heawood restriction this paper studies. The relevant
|
||||
%% classical input is Heawood's face-sum identity \cite{Heawood1898}; the goal
|
||||
%% here is to record what it forces on the dual of a (nested) tire graph.
|
||||
|
||||
\section{Heawood restrictions on the tire dual}
|
||||
\label{sec:heawood-restrictions}
|
||||
|
||||
%% TODO: main development.
|
||||
|
||||
\begin{thebibliography}{9}
|
||||
|
||||
\bibitem{Heawood1898}
|
||||
P.~J.~Heawood,
|
||||
\emph{On the four-colour map theorem},
|
||||
Quart. J.~Pure Appl. Math. \textbf{29} (1898), 270--285.
|
||||
|
||||
\bibitem{bauerfeld-depth}
|
||||
E.~Bauerfeld,
|
||||
\emph{Plane Depth},
|
||||
manuscript (math-research repository), 2026.
|
||||
|
||||
\bibitem{bauerfeld-nested-tires}
|
||||
E.~Bauerfeld,
|
||||
\emph{Nested Tire Decompositions of Plane Triangulations},
|
||||
manuscript (math-research repository), 2026.
|
||||
|
||||
\bibitem{bauerfeld-nested-tire-duals}
|
||||
E.~Bauerfeld,
|
||||
\emph{Coloring Nested Tire Dual Graphs},
|
||||
manuscript (math-research repository), 2026.
|
||||
|
||||
\end{thebibliography}
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user