On the existence of specified cycles in bipartite tournaments
نویسندگان
چکیده
For two integers n ≥ 3 and 2 ≤ p ≤ n, we denote D(n, p) the digraph obtained from a directed n-cycle by changing the orientations of p − 1 consecutive arcs. In this paper, we show that a family of k-regular (k ≥ 3) bipartite tournament BT4k contains D(4k, p) for all 2 ≤ p ≤ 4k unless BT4k is isomorphic to a digraph D such that (1, 2, 3, ..., 4k, 1) is a Hamilton cycle and (4m+ i− 1, i) ∈ A(D) and (i, 4m + i+ 1) ∈ A(D), where 1 ≤ m ≤ k − 1.
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