On the existence of specified cycles in bipartite tournaments

2017/06/20 by Zhang, Bo, Yang, Weihua
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.06526

Abstract

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 BT_4k contains D(4k,p) for all 2≤ p≤ 4k unless BT_4k 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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