Geodesic
Extremal Digraphs Avoiding Distinct Walks of Length 4 with the Same Endpoints
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 985-1004

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Let n ≥ 8 be an integer. We characterize the extremal digraphs of order n with the maximum number of arcs avoiding distinct walks of length 4 with the same endpoints.
Keywords: digraph, Turán problems, transitive tournament, walk 
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     author = {Lyu, Zhenhua},
     title = {Extremal {Digraphs} {Avoiding} {Distinct} {Walks} of {Length} 4 with the {Same} {Endpoints}},
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Lyu, Zhenhua. Extremal Digraphs Avoiding Distinct Walks of Length 4 with the Same Endpoints. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 985-1004. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a18/