didericis
c98a01b7f9
Adds tree_structure_sweep.py running the parent-child detection on
ALL 6-edge cuts found by greedy BFS-search on:
- 6 Holton-McKay non-Hamiltonian cubic plane graphs (HM #0-5).
- Dodecahedron (cubic dual of icosahedron, which is a min-degree-5
max planar graph).
Total 743 distinct 6-edge cuts × 2 sides each = 1486 tests.
Total cut tires examined: 11,477.
Tree-structure failures (cycles in parent relation): 0.
Per-graph cut counts:
HM #0: 128 cuts (all trees both sides)
HM #1: 127, HM #2: 122, HM #3: 123, HM #4: 101, HM #5: 97
Dodecahedron: 45 cuts (all trees both sides)
NOTE on the user's request: strictly "min-deg-5 with vertex-conn-6"
maximal planar graphs are incompatible (max planar avg deg < 6 ⇒
some vertex has degree ≤ 5 ⇒ vertex conn ≤ 5). Test coverage thus
includes:
- HM duals (21-vertex max planar, min-deg 4, vertex-conn 3): close
to the 4CT-relevant configurations.
- Icosahedron (12-vertex 5-regular, vertex-conn 5): min-deg 5
case.
Bug fix: previous cycle-detection logic in is_tree() always reported
a false-positive cycle (it added the current node to seen, then
trivially checked "cur in seen" after exit). Replaced with a clean
walk-up-from-each-node algorithm that detects actual cycles only.
Adds:
experiments/tree_structure_sweep.py
experiments/tree_structure_sweep_data.txt
Updates notes/cut_tire_tree_structure.tex with broader sweep table
and totals. Note grows to 4 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
math-research
Personal mathematics research repository by Eric Bauerfeld. Papers are written in AMS-LaTeX using the amsart document class.
Papers
kempe_style_search_for_smaller_contradiction
Humans Suffice: A Novel Proof of the Four Color Theorem
An in-progress proof of the Four Color Theorem via a minimal counterexample argument. The paper builds on Kempe's 1879 strategy — establishing valid cases for vertices of degree ≤ 4, then extending the argument to the degree-5 case using properties of non-adjacent degree-5 vertices, merged subgraphs, and locked colorings.
plane_depth_labelling
Plane Depth Labelling
Early-stage paper. Title and author information set; content in progress.
Creating a New Paper
Use run.sh to scaffold a new paper from the AMS-LaTeX template:
./run.sh init_paper "Your Paper Title"
This creates a new directory (name derived from the title) containing a paper.tex pre-filled with the title and author.
Setup
The Python library code in lib/ requires SageMath. Run setup once per machine:
./run.sh setup <sage_python_path> <sage_site_packages> [system_name]
sage_python_path— path to the SageMath Python interpreter (e.g./opt/sage/local/bin/python3)sage_site_packages— path to SageMath's site-packages directorysystem_name— optional label for this machine (defaults tohostname -s); used to store per-machine env files as.env.<system_name>
On subsequent runs the paths default to whatever was saved in .env, so ./run.sh setup alone re-runs setup with the existing configuration.
Setup also compiles the plantri submodule via make.
Running Sage
To run a Sage script with plantri available on PATH:
./run.sh sage <script.py> [args...]
Or to open an interactive Sage session:
./run.sh sage
Linting
./run.sh lint
Runs pyright and pylint on lib/ using the SageMath Python interpreter.
Shell Completion
To enable tab-completion for run.sh in zsh, add this to your .zshrc:
eval "$(path/to/run.sh completion)"
Or source it once in the current shell session:
eval "$(./run.sh completion)"
Building
Papers are compiled with LaTeX. From within a paper directory:
latexmk -pdf paper.tex