Paths with two blocks in \(n\)-chromatic digraphs
Let \(k+l=n-1 \geq 3\) and let \(D\) be an \(n\)-chromatic digraph. Proving a conjecture of El-Sahili, the authors show that \(D\) contains a \(P(k,l).\) (Here \(P(k,l)\) is an oriented path of order \(k+l+1\) starting with \(k\) forward arcs and followed by \(l\) backward arcs for some \(k \geq 1\) and \(l\geq 1.\)) Several connections to related results and open problems are mentioned.
scientific article; zbMATH DE number 5162681