Manuel Alejandro Juárez-Camacho

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Let D = (V (D), A(D)) be a digraph and k ≥ 2 an integer. We say that D is k-quasi-transitive if for every directed path (v0, v1, . . . , vk) in D we have (v0, vk) ∈ A(D) or (vk, v0) ∈ A(D). Clearly, a 2-quasi-transitive digraph is a quasi-transitive digraph in the usual sense. Bang-Jensen and Gutin proved that a quasi-transitive digraph D has a 3-king if(More)
On the existence and number of (k + 1)-kings in k-quasi-transitive digraphs. Abstract Let D = (V (D), A(D)) be a digraph and k ≥ 2 an integer. We say that D is k-quasi-transitive if for every directed path (v 0 , v 1 ,. .. , v k) in D, then (v 0 , v k) ∈ A(D) or (v k , v 0) ∈ A(D). Clearly, a 2-quasi-transitive digraph is a quasi-transitive digraph in the(More)
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