Year: 2026
Type: preprint
Abstract: Kelly's conjecture asks whether every regular tournament admits a Hamilton cycle decomposition. Motivated by its symmetry-preserving extension, we study cyclic Hamilton decompositions of carousel tournaments. For an odd integer $n$, let \[ T_n=\Cay\left( \mathbb Z_n,\left\{1,2,\ldots,\frac{n-1}{2}\right\} \right) \] be the carousel tournament. We ask whether $T_n$ has a Hamilton decomposition invariant under translation by $1$. Although the answer is immediate when $n$ is prime, composite orders introduce a genuine obstruction: nonunit differences generate short cycles rather than Hamilton cycles. We resolve a general composite-order family by proving that, whenever $n=pq$ for primes $7\le p
Source: arXiv (Cornell University)
Authors: Liao, Hongci, Peng, Yongju, Li, Guang, Ma, Yingbin
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3450710593, G761437261
OpenAlex ID: W7221015483