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    Wyświetlanie 1-8 z 8
    Tytuł:
    Antipodal Edge-Colorings of Hypercubes
    Autorzy:
    West, Douglas B.
    Wise, Jennifer I.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343560.pdf
    Data publikacji:
    2019-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    antipodal edge-coloring
    hypercube
    monochromatic geodesic
    Opis:
    Two vertices of the k-dimensional hypercube Qk are antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y. An antipodal edge-coloring of Qk is a 2- edge-coloring such that antipodal edges always have different colors. Norine conjectured that for k ≥ 2, in every antipodal edge-coloring of Qk some two antipodal vertices are connected by a monochromatic path. Feder and Subi proved this for k ≤ 5. We prove it for k ≤ 6.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 1; 271-284
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Well-Covered Direct Products
    Autorzy:
    Kuenzel, Kirsti
    Rall, Douglas F.
    Powiązania:
    https://bibliotekanauki.pl/articles/32315158.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    well-covered graph
    direct product of graphs
    isolatable vertex
    Opis:
    A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products. In particular, they showed that both factors of a well-covered direct product are also well-covered and proved that the direct product of two complete graphs (respectively, two cycles) is well-covered precisely when they have the same order (respectively, both have order 3 or 4). Furthermore, they proved that the direct product of two well-covered graphs with independence number one-half their order is well-covered. We initiate a characterization of nontrivial connected well-covered graphs G and H, whose independence numbers are strictly less than one-half their orders, such that their direct product G × H is well-covered. In particular, we show that in this case both G and H have girth 3 and we present several infinite families of such well-covered direct products. Moreover, we show that if G is a factor of any well-covered direct product, then G is a complete graph unless it is possible to create an isolated vertex by removing the closed neighborhood of some independent set of vertices in G.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 627-640
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Graphs with Disjoint Dominating and 2-Dominating Sets
    Autorzy:
    Henning, Michael A.
    Rall, Douglas F.
    Powiązania:
    https://bibliotekanauki.pl/articles/30146715.pdf
    Data publikacji:
    2013-03-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    2-domination
    vertex partition
    Opis:
    A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair. We provide a constructive characterization of trees that have a DD2-pair and show that K3,3 is the only connected graph with minimum degree at least three for which D ∪ D2 necessarily contains all vertices of the graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 1; 139-146
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
    Autorzy:
    Lu, Xiaoyun
    West, Douglas B.
    Powiązania:
    https://bibliotekanauki.pl/articles/31340879.pdf
    Data publikacji:
    2016-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    4-connected planar graph
    Hamiltonian-connected
    Tutte-path
    Opis:
    We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 3; 555-564
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Protection of Lexicographic Product Graphs
    Autorzy:
    Klein, Douglas J.
    Rodríguez-Velázquez, Juan A.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361746.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    lexicographic product
    weak Roman domination
    secure domination
    total domination
    double total domination
    Opis:
    In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight bounds and closed formulas for these parameters.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 139-158
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Survey on Packing Colorings
    Autorzy:
    Brešar, Boštjan
    Ferme, Jasmina
    Klavžar, Sandi
    Rall, Douglas F.
    Powiązania:
    https://bibliotekanauki.pl/articles/31804166.pdf
    Data publikacji:
    2020-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    packing coloring
    packing chromatic number
    subcubic graph
    S -packing chromatic number
    computational complexity
    Opis:
    If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . . such that for each pair of distinct vertices in the set Xi, the distance between them is larger than ai. If there exists an integer k such that V (G) = X1 ∪ ∪ Xk, then the partition is called an S-packing k-coloring. The S-packing chromatic number of G is the smallest k such that G admits an S-packing k-coloring. If ai = i for every i, then the terminology reduces to packing colorings and packing chromatic number. Since the introduction of these generalizations of the chromatic number in 2008 more than fifty papers followed. Here we survey the state of the art on the packing coloring, and its generalization, the S-packing coloring. We also list several conjectures and open problems.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 4; 923-970
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The 1,2,3-Conjecture and 1,2-Conjecture for sparse graphs
    Autorzy:
    Cranston, Daniel W.
    Jahanbekam, Sogol
    West, Douglas B.
    Powiązania:
    https://bibliotekanauki.pl/articles/30148718.pdf
    Data publikacji:
    2014-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    reducible configuration
    discharging method
    1, 2, 3-Conjecture
    1, 2-Conjecture
    Opis:
    The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms the conjectures for graphs with maximum average degree less than 8/3. The conjectures are already confirmed for larger families, but the structure theorems and reducibility results are of independent interest.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 4; 769-799
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Framework to Approach Vizing’s Conjecture
    Autorzy:
    Brešar, Boštjan
    Hartnell, Bert L.
    Henning, Michael A.
    Kuenzel, Kirsti
    Rall, Douglas F.
    Powiązania:
    https://bibliotekanauki.pl/articles/32222699.pdf
    Data publikacji:
    2021-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cartesian product
    total domination
    Vizing’s conjecture
    Clark and Suen bound
    Opis:
    We introduce a new setting for dealing with the problem of the domination number of the Cartesian product of graphs related to Vizing’s conjecture. The new framework unifies two different approaches to the conjecture. The most common approach restricts one of the factors of the product to some class of graphs and proves the inequality of the conjecture then holds when the other factor is any graph. The other approach utilizes the so-called Clark-Suen partition for proving a weaker inequality that holds for all pairs of graphs. We demonstrate the strength of our framework by improving the bound of Clark and Suen as follows: $ \gamma (X \square Y) \ge \max \{\frac{1}{2} \gamma (X) \gamma_t (Y), \frac{1}{2} \gamma_t (X) \gamma (Y) \} $, where $ \gamma $ stands for the domination number, $ \gamma_t $ is the total domination number, and $ X \square Y $ is the Cartesian product of graphs $X$ and $Y$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 3; 749-762
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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