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    Wyświetlanie 1-7 z 7
    Tytuł:
    A sufficient condition for the existence of k-kernels in digraphs
    Autorzy:
    Galeana-Sánchez, H.
    Rincón-Mejía, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/744223.pdf
    Data publikacji:
    1998
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    kernel
    k-kernel
    Opis:
    In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with l(γ) ≢ 0 (mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has four short chords. Then D has a k-kernel.
    This result generalizes some previous results on the existence of kernels and k-kernels in digraphs. In particular, it generalizes the following Theorem of M. Kwaśnik [5]: Let D be a strongly connected digraph, if every directed cycle of D has length ≡ 0 (mod k), k ≥ 2. Then D has a k-kernel.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1998, 18, 2; 197-204
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of (k,l)-kernels in infinite digraphs: A survey
    Autorzy:
    Galeana-Sánchez, H.
    Hernández-Cruz, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/30148241.pdf
    Data publikacji:
    2014-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    kernel
    k-kernel
    infinite digraph
    (k, l)-kernel
    Opis:
    Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction was done for (2, 1)-kernels, we present many original results concerning (k, l)-kernels for distinct values of k and l. The original results are sufficient conditions for the existence of (k, l)- kernels in diverse families of infinite digraphs. Among the families that we study are: transitive digraphs, quasi-transitive digraphs, right/left pretransitive digraphs, cyclically k-partite digraphs, κ-strong digraphs, k-transitive digraphs, k-quasi-transitive digraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 3; 431-466
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyclically k-partite digraphs and k-kernels
    Autorzy:
    Galeana-Sánchez, Hortensia
    Hernández-Cruz, César
    Powiązania:
    https://bibliotekanauki.pl/articles/743833.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    kernel
    (k,l)-kernel
    k-kernel
    cyclically k-partite
    Opis:
    Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.
    A (k,l)-kernel N of D is a k-independent set of vertices (if u,v ∈ N then d(u,v) ≥ k) and l-absorbent (if u ∈ V(D)-N then there exists v ∈ N such that d(u,v) ≤ l). A k-kernel is a (k,k-1)-kernel. A digraph D is cyclically k-partite if there exists a partition ${V_i}_{i = 0}^{k-1}$ of V(D) such that every arc in D is a $V_i V_{i+1}-arc$ (mod k). We give a characterization for an unilateral digraph to be cyclically k-partite through the lengths of directed cycles and directed cycles with one obstruction, in addition we prove that such digraphs always have a k-kernel. A study of some structural properties of cyclically k-partite digraphs is made which bring interesting consequences, e.g., sufficient conditions for a digraph to have k-kernel; a generalization of the well known and important theorem that states if every cycle of a graph G has even length, then G is bipartite (cyclically 2-partite), we prove that if every cycle of a graph G has length ≡ 0 (mod k) then G is cyclically k-partite; and a generalization of another well known result about bipartite digraphs, a strong digraph D is bipartite if and only if every directed cycle has even length, we prove that an unilateral digraph D is bipartite if and only if every directed cycle with at most one obstruction has even length.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 1; 63-78
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ
    Autorzy:
    Kucharska, Magdalena
    Kwaśnik, Maria
    Powiązania:
    https://bibliotekanauki.pl/articles/743435.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    kernel
    semikernel
    (k,l)-kernel
    Opis:
    The concept of (k,l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [4] proved a sufficient condition for a digraph to have a (k,l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k,l)-kernel. We restrict our attention to special superdigraphs of digraphs Pₘ and Cₘ.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2001, 21, 1; 95-109
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On (k,l)-kernel perfectness of special classes of digraphs
    Autorzy:
    Kucharska, Magdalena
    Powiązania:
    https://bibliotekanauki.pl/articles/744319.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    kernel
    (k,l)-kernel
    kernel-perfect digraph
    Opis:
    In the first part of this paper we give necessary and sufficient conditions for some special classes of digraphs to have a (k,l)-kernel. One of them is the duplication of a set of vertices in a digraph. This duplication come into being as the generalization of the duplication of a vertex in a graph (see [4]). Another one is the D-join of a digraph D and a sequence α of nonempty pairwise disjoint digraphs. In the second part we prove theorems, which give necessary and sufficient conditions for special digraphs presented in the first part to be (k,l)-kernel-perfect digraphs. The concept of a (k,l)-kernel-perfect digraph is the generalization of the well-know idea of a kernel perfect digraph, which was considered in [1] and [6].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 103-119
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    k-kernels in generalizations of transitive digraphs
    Autorzy:
    Galeana-Sánchez, Hortensia
    Hernández-Cruz, César
    Powiązania:
    https://bibliotekanauki.pl/articles/743887.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    kernel
    (k,l)-kernel
    k-kernel
    transitive digraph
    quasi-transitive digraph
    right-pretransitive digraph
    left-pretransitive digraph
    pretransitive digraph
    Opis:
    Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.
    A (k,l)-kernel N of D is a k-independent set of vertices (if u,v ∈ N, u ≠ v, then d(u,v), d(v,u) ≥ k) and l-absorbent (if u ∈ V(D)-N then there exists v ∈ N such that d(u,v) ≤ l). A k-kernel is a (k,k-1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are generalizations of transitive digraphs. In this paper the following results are proved: Let D be a right-(left-) pretransitive strong digraph such that every directed triangle of D is symmetrical, then D has a k-kernel for every integer k ≥ 3; the result is also valid for non-strong digraphs in the right-pretransitive case. We also give a proof of the fact that every quasi-transitive digraph has a (k,l)-kernel for every integers k > l ≥ 3 or k = 3 and l = 2.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 293-312
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Complexity of the 3-Kernel Problem in Some Classes of Digraphs
    Autorzy:
    Hell, Pavol
    Hernández-Cruz, César
    Powiązania:
    https://bibliotekanauki.pl/articles/30147225.pdf
    Data publikacji:
    2014-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    kernel
    3-kernel
    NP-completeness
    multipartite tournament
    cyclically 3-partite digraphs
    k-quasi-transitive digraph
    Opis:
    Let D be a digraph with the vertex set V (D) and the arc set A(D). A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V (D) − N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent subset of V (D). A 2-kernel is called a kernel. It is known that the problem of determining whether a digraph has a kernel (“the kernel problem”) is NP-complete, even in quite restricted families of digraphs. In this paper we analyze the computational complexity of the corresponding 3-kernel problem, restricted to three natural families of digraphs. As a consequence of one of our main results we prove that the kernel problem remains NP-complete when restricted to 3-colorable digraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 1; 167-185
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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