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Componentwise Complementary Cycles in Multipartite Tournaments

The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n 〉 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Le...

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Published in:Acta Mathematicae Applicatae Sinica 2012, Vol.28 (1), p.201-208
Main Authors: He, Zhi-hong, Li, Guo-jun, Zhou, Xue-qin
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description The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n 〉 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite (n 〉 6) tournament that is not a tournament. Let C be a 3-cycle of D and D / V(C) be nonstrong. For the unique acyclic sequence D1, D2,..., Da of D / V(C), where a 〉 2, let Dc = {Di|Di contains cycles, i = 1,2,...,a}, Dc = {D1,D2,...,Da} / De. If Dc≠ 0, then D contains a pair of componentwise complementary cycles.
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subjects Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
互补
循环
有向图
比赛
非周期性
title Componentwise Complementary Cycles in Multipartite Tournaments
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