Renames the paper directory and updates:
- \title in papers/coloring_nested_tire_dual_graphs/paper.tex:
"Coloring Nested Tire Graphs" → "Coloring Nested Tire Dual Graphs"
- bibliography reference in papers/plane_depth/paper.tex
- rebuilt both PDFs
The new title reflects that the paper studies the cubic DUAL of
maximal planar graphs (nested tire structure on G^*), not the
primal triangulation.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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>
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>
didericis