- 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>
Add 21-vertex and 24-vertex examples showing recursive lopsidedness
at d=2. Empirically confirm that the iterated algorithm (balanced
switch when available, preprocess otherwise) drives every face to
depth 0 on all tested configurations. Frame the remaining open
question as identifying a strictly-decreasing monovariant under
unbalanced preprocessing switches.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Defines level cycles, edge switches, surface switches, and facial depth
on level components of plane triangulations. Proves outerplanarity of
level components and a depth-descent lemma. Introduces balanced surface
switches and proves they remove a depth-d level cycle while creating
1-2 new depth-(d-1) cycles. Documents the 9-vertex counterexample where
no balanced switch exists and sketches preprocessing toward
balancedness, leaving general termination open.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis