didericis
c599975290
Standalone 4-page LaTeX note in notes/menagerie.tex with figures
generated by notes/generate_figures.py, summarizing edge 3-coloring
counts for the menagerie of subcubic outerplanar graphs:
- Path P_n: P_e(P_n, 3) = 3 · 2^{n-2}.
- Cycle C_n: P_e(C_n, 3) = 2^n + 2(-1)^n.
- Star K_{1,3}: P_e = 6.
- Corona C_n ∘ K_1: same as C_n (leaves are forced).
- Trees with Δ ≤ 3: product over BFS-order via greedy.
- 2-connected blocks: just cycles (chords force Δ > 3 generically).
- Block-cut tree decomposition for general subcubic outerplanar.
- Outside the menagerie: theta(2,2,2) = K_{2,3} (not outerplanar),
which is the interior-dual structure of D(T) when O has a bridge.
The note is meant as a quick reference for the partial-tire-dual
paper, particularly for the spoke-only case (corona) and as
motivation for the theta-graph carve-out in the bridge case.
6 small PNG figures included.
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
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eval "$(path/to/run.sh completion)"
Or source it once in the current shell session:
eval "$(./run.sh completion)"
Building
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latexmk -pdf paper.tex