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Prove intertwining-tree ⟺ Hamiltonian-dual; test the 6 Holton-McKay duals

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- 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>
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didericis
2026-05-21 20:59:13 -04:00
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papers/even_level_graph_generators/paper.aux
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\newlabel{sec:even-level-graphs}{{4}{3}{Even Level Graphs}{section.4}{}}
\newlabel{def:even-level-graph}{{4.1}{3}{Even Level Graph}{theorem.4.1}{}}
\newlabel{thm:even-level-4colorable}{{4.2}{3}{}{theorem.4.2}{}}
\citation{holton-mckay}
\newlabel{def:derived-level-graph}{{4.3}{4}{Derived level graph}{theorem.4.3}{}}
\newlabel{def:intertwining-tree}{{4.4}{4}{Intertwining tree}{theorem.4.4}{}}
\newlabel{thm:intertwining-iff-hamiltonian-dual}{{4.5}{4}{}{theorem.4.5}{}}
\newlabel{conj:every-triangulation-derived}{{4.6}{4}{}{theorem.4.6}{}}
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