PreprintCC BY 4.0arXiv
Cycles in Regular Multipartite Tournaments
Abstract
We study balanced cycles in regular multipartite tournaments. A cycle in a c-partite tournament is k-balanced if it contains exactly k vertices from each partite class. We prove that there exists an absolute integer r0 such that every regular c-partite tournament with each partite class size of r≥ r0 contains a k-balanced cycle for every 1≤ k≤ r when c=3 or c≥5, and for every 2≤ k≤ r when c=4. In particular, our result confirms three conjectures of Volkmann and Winzen for large regular multipartite tournaments. We also confirm Yeo's conjecture on the existence of (p,q)-cycle factors for large regular c-partite tournaments G with c≥4, where a (p,q)-cycle factor is a pair of vertex-disjoint cycles of lengths p and q spanning G.
Related
BibTeX
@misc{chang2026cycles,
title = {{Cycles in Regular Multipartite Tournaments}},
author = {Yufei Chang and Zhilan Wang and Shuo Wei and Jin Yan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06468},
eprint = {2611.06468},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06468},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cycles in Regular Multipartite Tournaments
AU - Yufei Chang
AU - Zhilan Wang
AU - Shuo Wei
AU - Jin Yan
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06468
UR - https://arxiv.org/abs/2611.06468
AB - We study balanced cycles in regular multipartite tournaments. A cycle in a c-partite tournament is k-balanced if it contains exactly k vertices from each partite class. We prove that there exists an absolute integer r_0 such that every regular c-partite tournament with each partite class size of r≥ r_0 contains a k-balanced cycle for every 1≤ k≤ r when c=3 or c≥5, and for every 2≤ k≤ r when c=4. In particular, our result confirms three conjectures of Volkmann and Winzen for large regular multipartite tournaments. We also confirm Yeo's conjecture on the existence of (p,q)-cycle factors for large regular c-partite tournaments G with c≥4, where a (p,q)-cycle factor is a pair of vertex-disjoint cycles of lengths p and q spanning G.
ER -