Longest paths through an arc in strong semicomplete multipartite digraphs
A digraph obtained by replacing each edge of a complete \(n\)-partite graph by an arc or a pair of mutually opposite arcs is called a semicomplete \(n\)-partite digraph. The author proves that every arc of a semicomplete \(n\)-partite digraph that belongs to an \(\ell\)-cycle \((\ell\geq 3)\) is in a path with at least \(\lceil{n+3\over 2}\rceil\) vertices.
scientific article; zbMATH DE number 1839039