On Disjoint Cycles of the Same Length in Tournaments  

作　　者：YUN WANG JIN YAN SHUO ZHU 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第2期271-281,共11页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12071260,11671232)。

摘　　要：A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups.In this paper,we investigate disjoint cycles of the same length in tournaments.In 2010,Lichiardopol conjectured that for given integers l≥3 and k≥1,any tournament with minimum out-degree at least(l-1)k-1 contains k disjoint l-cycles,where an l-cycle is a cycle of order l.Bang-Jensen et al.verified the conjecture for l=3 and Ma et al.proved that it also holds for l≥10.This paper provides a proof of the conjecture for the case of 9≥l≥4.

关 键 词：TOURNAMENTS minimum out-degree disjoint cycles 

分 类 号：O157.5[理学—数学]