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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
Full Text:
##### References:
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