Disjunction (every maximal planar graph is a derived level graph or
intertwining tree) holds through n=12. New intertwining-only iso class
at n=12 (analog of T*_9 at n=9) brings the count of derived-resistant
iso classes to 2 in this range. Per the intertwining-tree ⟺
Hamiltonian-dual equivalence, intertwining-tree failures cannot occur
until n=21 (dual of the 38-vertex Holton-McKay minimum Tait
counterexample).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
- New paper papers/even_level_graph_generators/: defines Even Level
Graph (every level cycle even), derived level graphs, intertwining
trees, and the disjunction conjecture (every maximal planar graph is
a derived level graph or intertwining tree). Empirically tested
through n=11: every iso class is at least an intertwining tree, so
the disjunction holds trivially in this range. The intertwining tree
disjunct fails at the Tutte graph dual (n=25), so the disjunction
becomes non-trivial past some unknown threshold.
- Level Switching paper: adds Section 4 (Reachability via edge
switches) with the two-step argument (Sleator-Tarjan-Thurston for
Case 1; face-merges for Case 2) and Theorem 4.1 (O(n) edge switches
suffice to reach all-depth-0).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis