6 research outputs found

    Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments

    Full text link
    A digraph such that every proper induced subdigraph has a kernel is said to be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI for short) resp.) if the digraph has a kernel (does not have a kernel resp.). The unique CKI-tournament is C→3\overrightarrow{C}_3 and the unique KP-tournaments are the transitive tournaments, however bipartite tournaments are KP. In this paper we characterize the CKI- and KP-digraphs for the following families of digraphs: locally in-/out-semicomplete, asymmetric arc-locally in-/out-semicomplete, asymmetric 33-quasi-transitive and asymmetric 33-anti-quasi-transitive TT3TT_3-free and we state that the problem of determining whether a digraph of one of these families is CKI is polynomial, giving a solution to a problem closely related to the following conjecture posted by Bang-Jensen in 1998: the kernel problem is polynomially solvable for locally in-semicomplete digraphs.Comment: 13 pages and 5 figure

    Master index to volumes 251-260

    Get PDF

    Subject Index Volumes 1–200

    Get PDF

    Cycle-pancyclism in bipartite tournaments I

    No full text
    Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T, and k an even number. In this paper, the following question is studied: What is the maximum intersection with γ of a directed cycle of length k? It is proved that for an even k in the range 4 ≤ k ≤ [(n+4)/2], there exists a directed cycle Ch(k)C_{h(k)} of length h(k), h(k) ∈ {k,k-2} with ∣A(Ch(k))∩A(γ)∣≥h(k)−3|A(C_{h(k)}) ∩ A(γ)| ≥ h(k)-3 and the result is best possible. In a forthcoming paper the case of directed cycles of length k, k even and k < [(n+4)/2] will be studied
    corecore