An improvement of Lichiardopol’s theorem on disjoint cycles in tournaments

Fuhong Ma and Jin Yan

Applied Mathematics and Computation, 2019, vol. 347, issue C, 162-168

Abstract: Let k ≥ 1 and q ≥ 3 be integers and let f(q)=(6q2−16q+10)/(3q2−3q−4). In this paper, we prove that if q ≥ 4, then every tournament T with both minimum out-degree and in-degree at least (q−1)k−1 contains at least f(q)k−2q disjoint cycles of length q. We also prove that if q=3 and k ≥ 6, then T contains at least 16k/15−5 disjoint triangles. Our results improve Lichiardopol’s theorem ([Discrete Math. 310 (19) (2010) 2567–2570]): for given integers q ≥ 3 and k ≥ 1, a tournament T with both minimum out-degree and in-degree at least (q−1)k−1 contains at least k disjoint cycles of length q.

Keywords: Tournaments; In-degree; Out-degree; Disjoint cycles (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318309603
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:162-168

DOI: 10.1016/j.amc.2018.10.086

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().