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math-research/papers/even_level_graph_generators/paper.log
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didericis 9bf4deac74 Prove intertwining-tree ⟺ Hamiltonian-dual; test the 6 Holton-McKay duals 
- Add Theorem: maximal planar G is an intertwining tree iff its dual
  G* is Hamiltonian (Tait-style Jordan-curve argument). Consequence:
  smallest non-intertwining-tree triangulations are the 6 duals of the
  38-vertex Holton-McKay graphs, at n=21.
- Load the 6 graphs from McKay's authoritative planar_code file
  (nonham38m4.pc), verified: 38 vertices, cubic, planar, non-Hamiltonian.
- All 6 duals confirmed not intertwining trees (exhaustive 2^20 check).
- 2 of 6 duals are themselves Even Level Graphs (sources 9, 10), hence
  derived level graphs -- first cases where the derived disjunct does
  work the intertwining-tree disjunct cannot.
- Remaining 4: bounded E/O-orbit search inconclusive; status open. This
  is the first genuinely undetermined instance of the conjecture.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
2026-05-21 20:59:13 -04:00

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