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k, l)-kernel k-kernel Transitive digraph Quasi-transitive digraph a b s t r a c t Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. In the literature, beautiful results describing the structure of both transitive and quasi-transitive digraphs are found that can be used to prove that every transitive digraph has a k-kernel for every k ≥ 2 and that every quasi-transitive digraph has a k-kernel for every k ≥ 3. We introduce three new families ofdoi:10.1016/j.disc.2012.05.005 fatcat:b7yrcy7imbdkpnmi5rd2wtiuqa