Files
math-research/papers/plane_depth/paper.aux
T
didericis 82f58f2f88 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 <noreply@anthropic.com>
2026-05-26 14:17:09 -04:00

30 lines
1.3 KiB
TeX

\relax
\citation{bauerfeld-pds-seq}
\citation{bauerfeld-nested-tires}
\citation{baker1994}
\@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: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}{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}}
\bibcite{baker1994}{1}
\bibcite{bauerfeld-pds-seq}{2}
\bibcite{bauerfeld-nested-tires}{3}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\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}