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    Wyświetlanie 1-4 z 4
    Tytuł:
    Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
    Autorzy:
    Affif Chaouche, Fatima
    Rutherford, Carrie G.
    Whitty, Robin W.
    Powiązania:
    https://bibliotekanauki.pl/articles/31339337.pdf
    Data publikacji:
    2015-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    extremal graph theory
    pancyclic graph
    Hamilton cycle
    Opis:
    It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of Ω(n1/k) on the growth rate.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 3; 533-539
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strongly pancyclic and dual-pancyclic graphs
    Autorzy:
    McKee, Terry
    Powiązania:
    https://bibliotekanauki.pl/articles/743097.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    pancyclic graph
    cycle extendable
    chordal graph
    pancyclic matroid
    dual-chordal graph
    Opis:
    Say that a cycle C almost contains a cycle C¯ if every edge except one of C¯ is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C¯ and every nonspanning cycle C is almost contained in another cycle C⁺. This is equivalent to requiring, in addition, that the sizes of C¯ and C⁺ differ by one from the size of C. Strongly pancyclic graphs are pancyclic and chordal, and their cycles enjoy certain interpolation and extrapolation properties with respect to almost containment. Much of this carries over from graphic to cographic matroids; the resulting 'dual-pancyclic' graphs are shown to be exactly the 3-regular dual-chordal graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 1; 5-14
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Alternating-Pancyclism in 2-Edge-Colored Graphs
    Autorzy:
    Cordero-Michel, Narda
    Galeana-Sánchez, Hortensia
    Powiązania:
    https://bibliotekanauki.pl/articles/32222696.pdf
    Data publikacji:
    2021-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    2-edge-colored graph
    alternating cycle
    alternating-pancyclic graph
    Opis:
    An alternating cycle in a 2-edge-colored graph is a cycle such that any two consecutive edges have different colors. Let $ G_1, . . ., G_k $ be a collection of pairwise vertex disjoint 2-edge-colored graphs. The colored generalized sum of $ G_1, . . ., G_k $, denoted by $ \oplus_{i=1}^k G_i $, is the set of all 2-edge-colored graphs $G$ such that: (i) \( V(G)= \bigcup _{i=1}^k V(G_i) \), (ii) $ G \langle V(G_i) \rangle \cong G_i $ for $ i = 1, . . ., k $ where $ G \langle V(G_i) \rangle $ has the same coloring as $ G_i $ and (iii) between each pair of vertices in different summands of $G$ there is exactly one edge, with an arbitrary but fixed color. A graph $G$ in $\oplus_{i=1}^k G_i $ will be called a colored generalized sum (c.g.s.) and we will say that $ e \in E(G) $ is an exterior edge if and only if \( e \in E(G) \backslash ( \bigcup_{i=1}^k E(G_i)) \). The set of exterior edges will be denoted by $ E_\oplus $. A 2-edge-colored graph $G$ of order $2n$ is said to be an alternating-pancyclic graph, whenever for each $ l \in {2, . . ., n} $, there exists an alternating cycle of length $2l$ in $G$. The topics of pancyclism and vertex-pancyclism are deeply and widely studied by several authors. The existence of alternating cycles in 2-edge-colored graphs has been studied because of its many applications. In this paper, we give sufficient conditions for a graph $ G \in \oplus_{i=1}^k G_i $ to be an alternating-pancyclic graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 3; 779-800
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two
    Autorzy:
    Hrnčiar, Pavel
    Monoszová, Gabriela
    Powiązania:
    https://bibliotekanauki.pl/articles/31342283.pdf
    Data publikacji:
    2018-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    self-centered graph with radius 2
    Hamiltonian graph
    pancyclic graph
    size of graph
    Opis:
    The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the minimum size of such graphs. For n ≤ 12 we have found the exact values of the minimum size. On the other hand, the exact value of the maximum size has been found for every n. Moreover, we have shown that such a graph (of order n and) of size m exists for every m between the minimum and the maximum size. For n ≤ 10 we have found all nonisomorphic graphs of the minimum size, and for n = 11 only for Hamiltonian graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 3; 661-681
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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