Moved from coloring_nested_tire_dual_graphs/ TO coloring_nested_tire_graphs/:
- Proposition (Source-side simple-cycle property) → now 1.7
- Lemma (Tire-component lemma) → now 1.8
- Theorem (Tire treads partition the bounded faces) → now 1.9
- Remark (boundaries-may-be-degenerate) → now 1.10
- Remark (no extra hypotheses needed) → now 1.11
These are foundational structural results about tire-graph
decompositions induced by a level source, not specifically about
the partial tire dual D(T) or coloring. Belongs in the
foundational paper.
Updates:
- Internal \cite[Definition~1.5]{bauerfeld-nested-tires} inside
the moved blocks → local \ref{def:tire-graph}.
- Foundational paper abstract rewritten to highlight the
tire-component lemma and tread partition as the main results.
- Dual paper abstract trimmed: no longer claims the tire-component
lemma as its own contribution.
- Dual paper intro citation list adds bullets for the moved
lemma (\cite[Lemma~1.8]) and theorem (\cite[Theorem~1.9]).
- No external references to the moved items inside the dual paper.
Page counts:
- Foundational: 3 → 7 pages.
- Dual: 9 → 7 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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