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split: extract foundational depth material into new plane_depth paper

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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>
This commit is contained in:
didericis
2026-05-26 13:49:44 -04:00
parent 1513922dec
commit 8b6c2b621c
12 changed files with 904 additions and 301 deletions
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[]\OT1/cmr/m/n/8 Building on the plane depth and quadri-lat-eral de-com-po-si-t
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