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Edge-chromatic 3-critical graphs — census data

This site documents the public research data repository for Le Chen and Songling Shan, Exploring the world 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. Orders 20 and 23 are intentionally marked pending.

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 pending computation pending

Even orders below 22 have no nontrivial survivors. The nontrivial-survivor counts for all odd orders through 21 are recorded in the census reported here. The order-22 survivor reproduces the Brinkmann--Steffen example.

Repository contents

  • results/ — per-order survivor census files named order_N_delta_3.json or order_N_delta_3.json.gz.
  • reports/ — audit JSON files recording independent checks and pipeline summaries.
  • code/ — the census pipeline plus classification and audit scripts, including code/scripts/classify_census_characterization.py (reproduces the paper's categorization table) and code/scripts/check_hashes.py (verifies the census SHA-256 hashes).
  • README.md — canonical census-file SHA-256 table and repository overview.