Cycles through large degree vertices in digraphs: A generalization of Meyniel's theorem
A set \(M\) of vertices of a digraph \(D\) is called a Meyniel set if \(d(u)+ d(v)\geq 2n-1\) for every pair of non-adjacent vertices belonging to \(M\) (\(n\) is the order of \(D\)). Generalizing Meyniel's theorem, the authors prove that every Meyniel set of a strongly connected digraph lies in a cycle. It is worth mentioning that insertion techniques used in the paper resemble those applied in \textit{J. Bang-Jensen}, \textit{G. Gutin} and \textit{J. Huang} [A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian, Discrete Math. 161, No. 1-3, 1-12 (1996; Zbl 0870.05046)] and some other papers by J. Bang-Jensen and G. Gutin with co-authors.
scientific article; zbMATH DE number 1234254