On the length of directed paths in digraphs
On the length of directed paths in digraphs
Thomass\'{e} conjectured the following strengthening of the well-known Caccetta-Haggkvist Conjecture: any digraph with minimum out-degree $\delta$ and girth $g$ contains a directed path of length $\delta(g-1)$. Bai and Manoussakis gave counterexamples to Thomass\'{e}'s conjecture for every even $g\geq 4$. In this note, we first generalize their counterexamples to show that …