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Paths with two blocks in \(k\)-chromatic digraphs. (English) Zbl 1050.05072
Summary: A block of a path in a digraph is a maximal directed subpath. We prove that any \(n\)-chromatic digraph contains a path of length \(n-1\) consisting of two blocks, one of which has length one. We then study the general problem of whether an \(n\)-chromatic digraph contains a path of length \(n-1\) consisting of two blocks of specified lengths.

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