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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.

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