标题：Every Cycle-Connected Multipartite Tournament with δ ≥ 2 Contains At Least Two Universal Arcs
作者：Zou, Q.;Li, G.;Gao, Y.
作者机构：[Zou, Q] Department of Mathematics, Xidian University, Xi'an, 710071, China;[ Li, G] School of Mathematics, Shandong University, Jinan, 250100, China; 更多
通讯作者地址：[Zou, QS]Xidian Univ, Dept Math, Xian 710071, Peoples R China.
来源：Graphs and combinatorics
关键词：Cycle-connected;Multipartite tournament;Universal arc
摘要：A digraph D = (V(D), A(D)) is called cycle-connected if for every pair of vertices u, v ∈ V(D) there exists a cycle containing both u and v. ádám (Acta Cybernet 14(1):1-12, 1999) proposed the question: Let D be a cycle-connected digraph. Does there exist a universal arc in D, i.e., an arc e ∈ A(D) such that for every vertex w ∈ V(D) there exists a cycle C in D containing both e and w?. Recently, Lutz Volkmann and Stefan Winzen have proved that this conjecture is true for multipartite tournaments. As an improvement of this result, we show in this note that every cycle-connected multipartite tournament with δ ≥ 2 contains at least two universal arcs.