didericis
8b6c2b621c
Splits the existing plane_depth_sequencing paper into two:
papers/plane_depth/paper.tex (NEW, 4 pages):
- Plane depth definition.
- Level edge, up/down/neutral triangle classification.
- Outerplanarity lemma (formerly Lemma 2.6 of PDS).
- Deep embedding G' definition.
- "Every face of G' is up or down" lemma.
- Unique level edge per face; shared level edge between adjacent faces.
- Quadrilateral decomposition definition with three types
(shallow diamond, deep diamond, S quad).
papers/plane_depth_sequencing/paper.tex (slimmed from 11 → 6 pages):
- Cites plane_depth for all foundational definitions.
- Keeps: slice, move definitions (anchor drop, level add, join,
ring completion), move selection, termination theorem.
papers/coloring_nested_tire_graphs/paper.tex:
- Bibliography updated: cite bauerfeld-depth instead of bauerfeld-pds.
- Two in-text references updated to cite the new outerplanarity
lemma in plane_depth.
Rationale: the outerplanarity / deep-embedding / quadrilateral-
decomposition material is foundational and reused by multiple
papers (and by the proposed level-cycle generalization). The
quadrilateral-sequencing programme is one specific application.
Splitting lets coloring_nested_tire_graphs cite the foundations
cleanly without dragging in the sequencing machinery.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
29 lines
1.3 KiB
TeX
29 lines
1.3 KiB
TeX
\relax
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\citation{bauerfeld-pds-seq}
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\citation{bauerfeld-nested-tires}
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\citation{baker1994}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Definitions}}{1}{}\protected@file@percent }
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\newlabel{def:plane-depth}{{1.1}{1}}
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\newlabel{def:level-edge}{{1.2}{1}}
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\newlabel{def:triangle-types}{{1.3}{1}}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Outerplanarity of depth levels}}{2}{}\protected@file@percent }
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\newlabel{lem:outerplanarity}{{2.1}{2}}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Deep embedding}}{2}{}\protected@file@percent }
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\newlabel{def:deep-embedding}{{3.1}{2}}
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\newlabel{lem:up-down-faces}{{3.2}{2}}
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\bibcite{baker1994}{1}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Quadrilateral decomposition}}{3}{}\protected@file@percent }
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\newlabel{lem:unique-level-edge}{{4.1}{3}}
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\newlabel{lem:shared-level-edge}{{4.2}{3}}
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\newlabel{def:quad-decomposition}{{4.3}{3}}
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\newlabel{def:quad-types}{{4.5}{3}}
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\bibcite{bauerfeld-pds-seq}{2}
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\bibcite{bauerfeld-nested-tires}{3}
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\newlabel{tocindent-1}{0pt}
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\newlabel{tocindent0}{12.7778pt}
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\newlabel{tocindent1}{17.77782pt}
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\newlabel{tocindent2}{0pt}
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\newlabel{tocindent3}{0pt}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{}\protected@file@percent }
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\gdef \@abspage@last{4}
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