Edge-chromatic 3-critical graphs — census data¶
This site documents the public research data repository for Le Chen and Songling Shan, Structure and census of edge-chromatic 3-critical graphs (2026). The repository contains census outputs, verification code, and audit reports supporting the paper's computational classification statements.
A nontrivial edge-chromatic 3-critical graph here means a graph that is connected, has maximum degree 3, has chromatic index 4, becomes 3-edge-colorable after deleting any edge, and has no 3-overfull subgraph.
Hash source of truth
The canonical SHA-256 values for census files live in the repository README.md. This site deliberately does not duplicate those hashes; CI checks the files against the README table.
Census results¶
The table records the number of nontrivial survivors for each order in the public census range.
| Order | Nontrivial survivors | Status |
|---|---|---|
| 4 | 0 | determined |
| 5 | 0 | determined |
| 6 | 0 | determined |
| 7 | 0 | determined |
| 8 | 0 | determined |
| 9 | 1 | determined |
| 10 | 0 | determined |
| 11 | 2 | determined |
| 12 | 0 | determined |
| 13 | 14 | determined here |
| 14 | 0 | determined |
| 15 | 94 | determined here |
| 16 | 0 | determined |
| 17 | 774 | determined here |
| 18 | 0 | determined |
| 19 | 6,984 | determined here |
| 20 | 0 | determined |
| 21 | 70,530 | determined here |
| 22 | 1 | Brinkmann--Steffen survivor reproduced |
| 23 | 782,186 | determined here |
| 24 | 9 | Brinkmann--Steffen count reproduced |
Even orders below 22 have no nontrivial survivors. The nontrivial-survivor counts for all odd orders through 23 are recorded here. The order-22 and order-24 computations reproduce the Brinkmann--Steffen counts; eight of the nine order-24 survivors are triangle blowups of the unique order-22 survivor, and the remaining order-24 graph is triangle-free.
Repository contents¶
results/— per-order survivor census files namedorder_N_delta_3.jsonororder_N_delta_3.json.gz.reports/— audit JSON files recording independent checks and pipeline summaries.code/— the census pipeline plus classification and audit scripts, includingcode/scripts/classify_census_characterization.py(reproduces the paper's categorization table) andcode/scripts/check_hashes.py(verifies the census SHA-256 hashes).README.md— canonical census-file SHA-256 table and repository overview.
Quick links¶
- Methodology — five-stage census pipeline.
- Data dictionary — JSON schema notes and loading snippet.
- Results gallery — per-order links and figure placeholders.
- Computational effort — Slurm telemetry for the completed Order-21, Order-22, and Order-23 campaigns.
- Interactive explorer — standalone explorer entry point.
- Verification — minimal reproduction instructions.
- Cite — paper and dataset citation text.