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dual_decomposition: iterated-reduction algorithm + Kempe/chord-apex search

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- Add section 3 with Algorithm 3.1 (iterated reduction with protected edges)
  and remarks on invariants and chord-apex applicability.
- Add fig:iterated-reduction-trace illustrating the algorithm on G' =
  dodecahedron (G' -> H_1 -> H_2 -> terminate).
- experiments/iterated_reduction.py: Sage implementation of the algorithm.
- experiments/draw_iterated_reduction.py: produces the 3 trace figures.
- experiments/check_dodecahedron_kempe.py: enumerate proper 3-edge-colorings
  of the dodecahedron's reduced dual and check the chord-apex + Kempe-cycle
  conditions (0 of 36 colorings satisfy all three).
- experiments/search_kempe_property.py: search across min-deg-5
  triangulations; the n = 14 first plantri triangulation is the smallest hit
  (reduced dual has 20 v, 30 e).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-23 12:40:38 -04:00
parent 192ad33bd2
commit c987259c14
11 changed files with 1057 additions and 55 deletions
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