Paths with two blocks in \(n\)-chromatic digraphs (Q885298)
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scientific article; zbMATH DE number 5162681
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Paths with two blocks in \(n\)-chromatic digraphs |
scientific article; zbMATH DE number 5162681 |
Statements
Paths with two blocks in \(n\)-chromatic digraphs (English)
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8 June 2007
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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.
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universal digraph
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unavoidable digraph
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\(n\)-chromatic digraph
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oriented path
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