From 82f58f2f880cf6a86d73595deaf2ef773b340a47 Mon Sep 17 00:00:00 2001 From: didericis Date: Tue, 26 May 2026 14:17:09 -0400 Subject: [PATCH] plane_depth: add level/interlevel dual edge definitions Extends Definition 1.2 (level edge) to also define "interlevel edge" for the primal, and adds Definition 1.3 (level/interlevel dual edge) classifying dual edges by whether they cross a level or interlevel primal edge. Useful downstream: in coloring_nested_tire_graphs, the partial tire dual's edges can now be classified cleanly as level or interlevel dual edges using the same vocabulary, instead of ad hoc "interior annular edge" / "spoke edge" naming. Paper stays at 4 pages. Co-Authored-By: Claude Opus 4.7 --- papers/plane_depth/paper.aux | 9 +++++---- papers/plane_depth/paper.log | 14 +++++++------- papers/plane_depth/paper.pdf | Bin 191936 -> 193466 bytes papers/plane_depth/paper.tex | 18 +++++++++++++++++- 4 files changed, 29 insertions(+), 12 deletions(-) diff --git a/papers/plane_depth/paper.aux b/papers/plane_depth/paper.aux index 6c7a65e..b0d5fa7 100644 --- a/papers/plane_depth/paper.aux +++ b/papers/plane_depth/paper.aux @@ -5,18 +5,18 @@ \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Definitions}}{1}{}\protected@file@percent } \newlabel{def:plane-depth}{{1.1}{1}} \newlabel{def:level-edge}{{1.2}{1}} -\newlabel{def:triangle-types}{{1.3}{1}} +\newlabel{def:level-dual-edge}{{1.3}{1}} +\newlabel{def:triangle-types}{{1.4}{1}} \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Outerplanarity of depth levels}}{2}{}\protected@file@percent } \newlabel{lem:outerplanarity}{{2.1}{2}} \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Deep embedding}}{2}{}\protected@file@percent } \newlabel{def:deep-embedding}{{3.1}{2}} -\newlabel{lem:up-down-faces}{{3.2}{2}} -\bibcite{baker1994}{1} +\newlabel{lem:up-down-faces}{{3.2}{3}} \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Quadrilateral decomposition}}{3}{}\protected@file@percent } \newlabel{lem:unique-level-edge}{{4.1}{3}} \newlabel{lem:shared-level-edge}{{4.2}{3}} \newlabel{def:quad-decomposition}{{4.3}{3}} -\newlabel{def:quad-types}{{4.5}{3}} +\bibcite{baker1994}{1} \bibcite{bauerfeld-pds-seq}{2} \bibcite{bauerfeld-nested-tires}{3} \newlabel{tocindent-1}{0pt} @@ -24,5 +24,6 @@ \newlabel{tocindent1}{17.77782pt} \newlabel{tocindent2}{0pt} \newlabel{tocindent3}{0pt} +\newlabel{def:quad-types}{{4.5}{4}} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{}\protected@file@percent } \gdef \@abspage@last{4} diff --git a/papers/plane_depth/paper.log b/papers/plane_depth/paper.log index 0526a94..1f066f0 100644 --- a/papers/plane_depth/paper.log +++ b/papers/plane_depth/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) 26 MAY 2026 13:47 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 26 MAY 2026 14:17 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -194,13 +194,13 @@ e [1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] [4] (./paper.aux) ) Here is how much of TeX's memory you used: - 2992 strings out of 478268 - 41730 string characters out of 5846347 - 342165 words of memory out of 5000000 - 21042 multiletter control sequences out of 15000+600000 + 2993 strings out of 478268 + 41751 string characters out of 5846347 + 341175 words of memory out of 5000000 + 21043 multiletter control sequences out of 15000+600000 475666 words of font info for 53 fonts, out of 8000000 for 9000 1302 hyphenation exceptions out of 8191 - 69i,6n,76p,242b,344s stack positions out of 10000i,1000n,20000p,200000b,200000s + 69i,6n,76p,242b,282s stack positions out of 10000i,1000n,20000p,200000b,200000s -Output written on paper.pdf (4 pages, 191936 bytes). +Output written on paper.pdf (4 pages, 193466 bytes). 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