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math-research/papers/even_level_graph_generators/paper.fls
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didericis b45c3d5510 even_level: extend conjecture test to the cyclically-5-connected case (n=24) 
Add the n=24 result to the Even Level Graph Generators paper: the dual of
the unique 44-vertex non-Hamiltonian cyclically-5-connected cubic planar
graph (Holton-McKay Fig. 2.10) -- a 24-vertex 5-connected triangulation,
the first conjecture test outside the 3-cut family -- is a bridge-derived
level graph, two verified bridge switches from an Even Level Graph
(source 19).

- Generate the graph rather than transcribe it: plantri -c5 lists all 6833
  5-connected 24-vertex triangulations; exactly one has a non-Hamiltonian
  dual, which also settles the uniqueness Holton-McKay left open at 44
  vertices (cyclically-5-connected triangulation <=> dual cubic graph).
- New abstract sentence + "cyclically-5-connected case: n=24" subsection,
  noting the classic 46-vertex Tutte graph is only cyclically 3-connected.
- Figure 6 (figures/fig210_dual.png): the dual T, parity-coloured, with the
  two introduced bridge edges {6,19} and {20,22} in green (style of Fig. 5).
- Experiments: test_fig210_dual_bridge.py (generate->filter->test pipeline),
  verify_fig210_witness.py (step-verifies the witness), draw_fig210_dual.py
  (figure), fig210_dual.g6 (the unique graph). paper.pdf rebuilt (10 pages).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-22 13:06:47 -04:00

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