- 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>
didericis
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