Repository (source code, run scripts, catalogues): https://github.com/LeAndr-Graph/P1F-Census
K18: there are exactly 10,710 pairwise non-isomorphic perfect 1-factorizations (P1Fs) of K18 with a non-trivial automorphism group (|Aut| > 1).
| |Aut| | 2 | 3 | 4 | 8 | 16 | 17 | 272 |
|---|---|---|---|---|---|---|---|
| classes | 10,179 | 351 | 144 | 22 | 12 | 1 | 1 |
Catalogue: AllResults/K18_P1F_aut_gt1.txt ·
dataset DOI 10.5281/zenodo.22238984 ·
runs: runs/K18/ · paper: submitted to Australas. J. Combin.
K20: there are exactly 149,836 pairwise non-isomorphic P1Fs of K20 with |Aut| >= 3: 230 with |Aut| > 3 and 149,606 with |Aut| = 3.
| |Aut| | 3 | 6 | 9 | 18 | 19 | 57 | 171 | 342 |
|---|---|---|---|---|---|---|---|---|
| classes | 149,606 | 168 | 46 | 9 | 3 | 1 | 2 | 1 |
Catalogues: AllResults/K20_P1F_aut_gt3.txt,
AllResults/K20_P1F_aut_eq3.txt.gz ·
dataset DOIs 10.5281/zenodo.22215011 (|Aut| > 3),
10.5281/zenodo.22880728 (|Aut| = 3) ·
runs: runs/K20/
Derived: 104,088 P1Fs of K17,17 from the K18 catalogue, 10.5281/zenodo.22548329.
Verification: the same engine reproduces the known K14 classification (Dinitz and Garnick, 1996)
and the K16 classes with |Aut| > 1 (Gill and Wanless, 2020):
AllResults/K14_P1F_aut_gt1.txt (21),
AllResults/K16_P1F_aut_gt1.txt (89),
runs/K14/, runs/K16/, regression/.
Andrei V. Ivanov, ORCID 0000-0002-1574-6716, died September 2026.
Leonid M. Tertitski, ORCID 0009-0002-7556-9552 (corresponding).
| Topic | File |
|---|---|
| definitions, catalogue format, record numbering, atomic Latin squares | AllResults/ReadMe.md |
| each computation: what it searches, expected result, runtime | ReadMe.md in each runs/ folder |
| theorems the search relies on (Ihrig 1986) | docs/theorems.md |
| build, configuration, regression suite | docs/build.md |
| what is open (K20 |Aut| = 2) | runs/K20/ReadMe.md |
Cite the dataset DOI for the graph in question, for example:
Ivanov, A. V., & Tertitski, L. M. (2026). Perfect one-factorizations of K18 with non-trivial automorphism group: a complete catalogue (Version 1.0.0) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.22238984
Questions, missing or extra classes, failed reproductions: open an issue.
Source code: MIT (LICENSE). Catalogues in AllResults/: CC0 1.0.