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Paths with two blocks in \(n\)-chromatic digraphs. (English) Zbl 1119.05049
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.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C15 Coloring of graphs and hypergraphs
05C38 Paths and cycles
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