From 30f28a60d679b60a686d527e39c5e07c824349bc Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 10:54:07 -0400 Subject: [PATCH] level_resolutions: add n=7 missing-isomorphism figures, rebuild PDF Add the figures for the n=7, idx=2 missing-isomorphism case (missing_iso_n7_idx2.png is included in paper.tex), plus its 4-coloring and level-decomposition companions and the G-for-T preimage graph. Rebuild paper.pdf and its LaTeX aux/log/out. Co-Authored-By: Claude Opus 4.7 (1M context) --- .../G_for_T_n7_idx2.png | Bin 0 -> 208738 bytes .../missing_iso_n7_idx2.png | Bin 0 -> 126586 bytes .../missing_iso_n7_idx2_4color.png | Bin 0 -> 52240 bytes .../missing_iso_n7_idx2_levels.png | Bin 0 -> 101245 bytes .../paper.aux | 28 ++-- .../paper.log | 149 ++++++++++++------ .../paper.out | 9 +- .../paper.pdf | Bin 270602 -> 353656 bytes 8 files changed, 119 insertions(+), 67 deletions(-) create mode 100644 papers/level_resolutions_of_maximal_planar_graphs/G_for_T_n7_idx2.png create mode 100644 papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2.png create mode 100644 papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_4color.png create mode 100644 papers/level_resolutions_of_maximal_planar_graphs/missing_iso_n7_idx2_levels.png diff --git a/papers/level_resolutions_of_maximal_planar_graphs/G_for_T_n7_idx2.png b/papers/level_resolutions_of_maximal_planar_graphs/G_for_T_n7_idx2.png new file mode 100644 index 0000000000000000000000000000000000000000..e6bec4824d32f06e4adf7d1ed545e87034d03894 GIT binary patch literal 208738 zcmdqJWmr{vw>PY^1ylqDQIHZ5=~kpckPwuTM(LDpX%VCarBO5jo;h>o@?)t-if7K? zsGT{3m4=HA{~|FiDF*-Hvlmyhe`aN5@1$#Mc;>0Dy|uZOy}7C0Ek{FJJ5wu5E>;e9 zR$k^?CieE$c6@AX7XS5suv*y~v)z^Wr4CoQU@fI?cjgSy3G(YKP6V&dnX_lkJbv_0 z=~div{Q2+1eFIIqmsz7{duZR;d)ueKenXFod+trd*<||Ly41LV8Asyc;*YLAyl_?i z%NPE?zEo5!^}BUd?9W>3b@FoA&Gw>?1-q=j7t&$0_>FRl9UsvLCgY0YQu|!_kKeQc zwmmNV&wuo}!l(AX{;}aqT&?u~`gy+3-jV-#MR);wQ5>fKb^pFi&}JFi3gzkWXc=l_3ibVGWmz)<|rBcIRud+U<~!3KTz z{KzJ6u31Z&Nk^`<$8t5&gbLj5NtKym@vRou)yyLPxuPe>1K_7T~u|LNw=vQYv|BG*B zuQrm~6S*yh)i!0P0*7286h~r2Y-d`oGKdvneWurTvcY}(eZj&tnoXOve%#~GqQh1A zV4jBbq=86I?K+j!TG1x2SFmSBNpr&H=~kEU4LQM`2zsr`@BTqSL|+wC3CnEJggF|; zgq}wme%e#hDkqiVlD8qnBSs{rJ`ckD|Dplqt(%}#vnG-Jf_^Jmd1 zK~DJij>kUwMt8Y`S>hD8Zrxw`wrFYfsIkatcuRpN$A>|?6Q0`4nk7%}nf$CtcM>w$ z>yZ`kx4_$YrxQV1Ws%EYVmZd>$)u7^U-vKmr?=!K1OO7?+ahTJ#@3=Dj7-y-lONhz$GMNMe zp`M>|A)Z(ORKts#&;0O6Z^tJ}lvz){F&WJJJeaTVcTYm!C}`_<@ZR1l4)+85p)?(p zEG>_{Nt_`{_oI#G+fP5)#>@RW1%A&H{5erQ>1POW$5p1bX8TNQ>o@;!_DRkGpL>?M@cIly5e` zYO_7BP&$A*Sj_4%bb7%^aU$8$C%Mrvxos!`B ztho;tnNoD-Y7|S~vl@Tyw)ul@(^WM^;zzW_>NlHpes_s0rhqUqO zON$;V{#3!LYTP#u#cm6sni@^U^`g#2eQX?ewtlaBmx}zA1ZI1)=rrM2$OOYhS$%rq z>Q}WEw@c|Ll>0XJ`-m_>AxoCh*W2j8&7k9s-UE}rsy1qbtY7WU{0K)+j8!<5HcGBh zIt_lhEc;8ZG4O}rW8L>Ve@(qXH}AYQe9IApYXfJxg8fnydjl%HW-RQjOIrys=dW|S zDP!m8~_4-9NZ_|QJHs_e>w!g`lD9@euyinx@$KliU z-n)yYbj$UMdSrIT2M)aSNiX{{ZAq;K2zG9wO*=l`7n<`Lw;~*-T;BKJ!fpP2zDNwU z>iP1KtO|xdIEr+c?Hx+2#C&Kb*qsG#4qe+t10VD+tZvN7;aasV*~N%1KS~!VAF|p& z&y1pG)U0sp9g(uab14%g@*ilBNmoby7CE{Nx3W}n-r&gp_;^3dbcmQi@ln9Lcgl>a z-?EFK0-cxhnHbjAuEJ}KkXWu)^lHUYov^6ck)&QzmDqCJS?rUBnn&+6 z1`>zc)YzpYC(o4CdgClfFHP3_q07#lzi5)?1Otz=5-wL_$E5mAsoZhpr7Pu$mFKJQ z9Ha);Ivz|!aGLgJe2929Ug?b9A1$+Ey21Kfep~MjWub9bl&M(NLp2x^<_qF64?5#` zQ@%V7ml)^wJaKD$=?lFpQP6Ufr*z;}sLkcgULtT+T^z zpNd{>=+QbX_HLHL1a4Vh?8_Qy^{=pc&A&X^VHF}`w{g~r6zw&32K>7%S%R3tCQbyT3=j13F`!&7BNi*7S`|Oe9vg*n%FmU zx$1>Y#yCvD+14k&hoNtb%oSLu7_ExLtqbr3%f|B=?w!EXYukpl*ybo3>fJYz zevoea`qvz8@WYtnG~YyiC)tp+uJ_d5_wYu%?Wdh%uFfpE3N&iU@kzeBnM!KO%__0! z*c!pGsnLF?_oK}j?=StqVe-~_AKz6RZ{3xRnC+~l$|43UuYDL>)rjTj*~@f+w(~%#l}uDfROgyQn~w~(O-fVxpc<5k&Ma)gQ3DF z8B6W}F;s3ouwM!RV%_fQ%tA66o5R3o%(&Ur4?({ z^x)a*)?aeME5Bd+MuKttaDM31N8{K5X%gC!Q9j&juUljUsd zQTkhRT{jLfE8(uiw6wH8wk}+_V5`lv-1ZfPbr{D2IB-=L1Nbq3&tcI&CMM=}

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{sec:flip-algorithm}. ``Algorithm output (any)'' counts iso-classes that appear as the iso-class of some labelled triangulation output of the algorithm; ``Simple level resolutions'' counts iso-classes that additionally satisfy the bipartite-parity condition of Definition~\ref {def:simple-level-resolution}}{table.2}{}} +\newlabel{obs:md5-simple-resolution}{{6.6}{7}{}{theorem.6.6}{}} +\newlabel{q:terminate-all-n}{{6.7}{7}{}{theorem.6.7}{}} +\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Discussion and open questions}}{7}{section.7}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces At $n = 7$, iso-class $T$ with degree sequence $(6, 5, 5, 5, 3, 3, 3)$ is not a simple level resolution. Left: $T$ drawn with face source $S = \{0, 1, 5\}$ outlined; vertices are labelled by their BFS level. Middle: the even-parity subgraph $E_{T,S}(T)$, induced on $\{0, 1, 5\}$, contains the source-face triangle (highlighted) — an odd cycle. Right: the odd-parity subgraph $O_{T,S}(T)$, induced on $\{2, 3, 4, 6\}$, contains a triangle on $\{2, 3, 6\}$ (highlighted). The obstruction is identical for every face source of $T$; vertex sources at degree-$3$ vertices produce $L_1$ triangles in the odd-parity subgraph.}}{8}{figure.1}\protected@file@percent } +\newlabel{fig:missing-iso}{{1}{8}{At $n = 7$, iso-class $T$ with degree sequence $(6, 5, 5, 5, 3, 3, 3)$ is not a simple level resolution. Left: $T$ drawn with face source $S = \{0, 1, 5\}$ outlined; vertices are labelled by their BFS level. Middle: the even-parity subgraph $E_{T,S}(T)$, induced on $\{0, 1, 5\}$, contains the source-face triangle (highlighted) — an odd cycle. Right: the odd-parity subgraph $O_{T,S}(T)$, induced on $\{2, 3, 4, 6\}$, contains a triangle on $\{2, 3, 6\}$ (highlighted). The obstruction is identical for every face source of $T$; vertex sources at degree-$3$ vertices produce $L_1$ triangles in the odd-parity subgraph}{figure.1}{}} +\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Implementation}}{8}{section.8}\protected@file@percent } +\newlabel{sec:impl}{{8}{8}{Implementation}{section.8}{}} \bibcite{appelhaken}{1} \bibcite{rsst}{2} \bibcite{tutte}{3} @@ -70,7 +70,5 @@ \newlabel{tocindent1}{18.3999pt} \newlabel{tocindent2}{29.38873pt} \newlabel{tocindent3}{0pt} -\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Implementation}}{9}{section.8}\protected@file@percent } -\newlabel{sec:impl}{{8}{9}{Implementation}{section.8}{}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{9}{section*.4}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{9}{section*.3}\protected@file@percent } \gdef \@abspage@last{9} diff --git a/papers/level_resolutions_of_maximal_planar_graphs/paper.log b/papers/level_resolutions_of_maximal_planar_graphs/paper.log index b7db483..a237bbd 100644 --- a/papers/level_resolutions_of_maximal_planar_graphs/paper.log +++ b/papers/level_resolutions_of_maximal_planar_graphs/paper.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 20 MAY 2026 13:47 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 20 MAY 2026 16:00 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -250,6 +250,26 @@ Package: enumitem 2019/06/20 v3.9 Customized lists \enit@count@id=\count282 \enitdp@description=\count283 ) +(/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/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=\dimen155 +\Gin@req@width=\dimen156 +) \c@theorem=\count284 (/usr/local/texlive/2022/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def @@ -260,36 +280,36 @@ File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX) (./paper.aux) \openout1 = `paper.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 59. -LaTeX Font Info: ... okay on input line 59. -LaTeX Font Info: Trying to load font information for U+msa on input line 59. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 60. +LaTeX Font Info: ... okay on input line 60. +LaTeX Font Info: Trying to load font information for U+msa on input line 60. 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