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Two Perfect One-Factorizations of K92
Abstract
A perfect 1-factorization of the complete graph K2t is a partition of its edges into perfect matchings such that the union of any two of them is a Hamilton cycle. Kotzig conjectured in 1963 that K2t has a perfect 1-factorization for every t ≥ 2, but apart from some infinite families and a list of sporadic orders the conjecture is open, and $92$ was one of the nine orders up to $100$ for which no perfect 1-factorization was known. In this paper we construct two non-isomorphic perfect 1-factorizations of K92.
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BibTeX
@misc{maciosowski2026perfect,
title = {{Two Perfect One-Factorizations of $K_92$}},
author = {Tomasz Maciosowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20408},
eprint = {2610.20408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20408},
}
RIS
TY - UNPB
TI - Two Perfect One-Factorizations of K_92
AU - Tomasz Maciosowski
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20408
UR - https://arxiv.org/abs/2610.20408
AB - A perfect 1-factorization of the complete graph K_2t is a partition of its edges into perfect matchings such that the union of any two of them is a Hamilton cycle. Kotzig conjectured in 1963 that K_2t has a perfect 1-factorization for every t ≥ 2, but apart from some infinite families and a list of sporadic orders the conjecture is open, and $92$ was one of the nine orders up to $100$ for which no perfect 1-factorization was known. In this paper we construct two non-isomorphic perfect 1-factorizations of K_92.
ER -