A NOTE ON REDUCIBLE CYCLES IN MULTIPARTITE TOURNAMENTS
Linqiang Pan, Zhengke Miao, Ke-Min Zhang · Taiwanese Journal of Mathematics · 2002
[3] proves that if $T$ is a strong $c$-partite tournament $(c\geq 3)$, then there is a $(k-3)$-reducible $k$-cycle in $T$, for all $k=3,4,\cdots, c$. In this paper we investigate the smallest number of $(k-3)$-reducible $k$-cycles in strong $c$-partite tournaments for $3\leq k\leq c$ and give some related problems.