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On short cycles in triangle-free oriented graphs

Yurong JiShufei WuHui Song — 2018

Czechoslovak Mathematical Journal

An orientation of a simple graph is referred to as an oriented graph. Caccetta and Häggkvist conjectured that any digraph on n vertices with minimum outdegree d contains a directed cycle of length at most n / d . In this paper, we consider short cycles in oriented graphs without directed triangles. Suppose that α 0 is the smallest real such that every n -vertex digraph with minimum outdegree at least α 0 n contains a directed triangle. Let ϵ < ( 3 - 2 α 0 ) / ( 4 - 2 α 0 ) be a positive real. We show that if D is an oriented graph without...

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