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In the paper we recall two different colourings of arcs of digraphs and associate them with two special colourings of arcs and vertices of digraphs, called pseudototal colourings of digraphs. We find pseudototal chromatic indices of transitive tournaments and of complete symmetric digraphs.
In a simple digraph, a star of degree t is a union of t edges with a common tail. The k-domination number γ k (G) of digraph G is the minimum number of stars of degree at most k needed to cover the vertex set. We prove that γ k (T)= n/(k+1) when T is a tournament with n>=14klgk vertices. This improves a result of Chen, Lu and West. We also give a short direct proof of the result...
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