Critical Kernel Imperfect Problem in Generalizations of Bipartite Tournaments
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Kernel is an important topic in digraphs. A digraph such that every proper induced subdigraph has a kernel is said to be critical kernel imperfect (CKI, for short) if the digraph does not have a kernel. Galeana-Sánchez and Olsen characterized the CKI-digraphs for the following families of digraphs: asymmetric arc-locally in-/out-semicomplete digraphs, asymmetric 3-quasi-transitive digraphs and asymmetric 3-anti-quasi-transitive \(TT_3\)-free digraphs. In this paper, we shall completely characterize the above four classes CKI-digraphs without any restriction on arcs and \(TT_3\)-free subdigraphs.
KeywordsKernel CKI-digraph Generalization of bipartite tournaments Arc-locally in-semicomplete digraph 3-Quasi-transitive digraph 3-Anti-quasi-transitive digraph
Mathematics Subject Classification05C20 05C69
The author thanks the anonymous referees for several helpful comments.
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