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    Wyświetlanie 1-4 z 4
    Tytuł:
    About uniquely colorable mixed hypertrees
    Autorzy:
    Niculitsa, Angela
    Voloshin, Vitaly
    Powiązania:
    https://bibliotekanauki.pl/articles/743697.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    colorings of graphs and hypergraphs
    mixed hypergraphs
    unique colorability
    trees
    hypertrees
    elimination ordering
    Opis:
    A mixed hypergraph is a triple = (X,,) where X is the vertex set and each of , is a family of subsets of X, the -edges and -edges, respectively. A k-coloring of is a mapping c: X → [k] such that each -edge has two vertices with the same color and each -edge has two vertices with distinct colors. = (X,,) is called a mixed hypertree if there exists a tree T = (X,) such that every -edge and every -edge induces a subtree of T. A mixed hypergraph is called uniquely colorable if it has precisely one coloring apart from permutations of colors. We give the characterization of uniquely colorable mixed hypertrees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2000, 20, 1; 81-91
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Open Locating-Dominating Sets in Circulant Graphs
    Autorzy:
    Givens, Robin M.
    Yu, Gexin
    Kincaid, Rex K.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361753.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    open locating-dominating sets
    circulant graphs
    Hall’s Matching Theorem
    mixed-weight open locating-dominating sets
    Opis:
    Location detection problems have been studied for a variety of applications including finding faults in multiprocessors, contaminants in public utilities, intruders in buildings and facilities, and for environmental monitoring using wireless sensor networks. In each of these applications, the system or structure can be modeled as a graph, and sensors placed strategically at a subset of vertices can locate and detect anomalies in the system. An open locating-dominating set (OLD-set) is a subset of vertices in a graph in which every vertex in the graph has a non-empty and unique set of neighbors in the subset. Sensors placed at OLD-set vertices can uniquely detect and locate disturbances in a system. These sensors can be expensive and, as a result, minimizing the size of the OLD-set is critical. Circulant graphs, a group of regular cyclic graphs, are often used to model parallel networks. We prove the optimal OLD-set size for a particular circulant graph using Hall’s Theorem. We also consider the mixed-weight OLD-set introduced in [R.M. Givens, R.K. Kincaid, W. Mao and G. Yu, Mixed-weight open locating-dominating sets, in: 2017 Annual Conference on Information Science and Systems, (IEEE, Baltimor, 2017) 1–6] which models a system with sensors of varying strengths. To model these systems, we place weights on the vertices in the graph, representing the strength of a sensor placed at the corresponding location in the system. We study particular mixed-weight OLD-sets in cycles, which behave similarly to OLD-sets in circulant graphs, and show the optimal mixed-weight OLD-set size using the discharging method.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 47-62
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graph models of automobile gears - kinematics
    Autorzy:
    Drewniak, J.
    Kopeć, J.
    Zawiślak, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/955206.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    analiza kinematyczna
    wskaźniki
    przekładnia zębata
    mechatronika samochodowa
    kinematical analysis
    ratios
    mixed graphs
    contour graphs
    bond graphs
    Opis:
    In the present paper, kinematical analysis of an automotive gear is described. Versatile graph based methods have been utilized for this purpose. An application of mixed, contour and bond graphs gives the same results. It allows the detection of possible mistakes as well as a deeper insight into the designed artifact. The graphs can also be used for further analyses which will be published in a separate document.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2014, 19, 3; 563-573
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    High Girth Hypergraphs with Unavoidable Monochromatic or Rainbow Edges
    Autorzy:
    Axenovich, Maria
    Karrer, Annette
    Powiązania:
    https://bibliotekanauki.pl/articles/32361723.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypergraph
    chromatic number
    mixed hypergraph
    bihyper-graphs
    monochromatic
    rainbow
    girth
    selective
    Opis:
    A classical result of Erdős and Hajnal claims that for any integers k, r, g ≥ 2 there is an r-uniform hypergraph of girth at least g with chromatic number at least k. This implies that there are sparse hypergraphs such that in any coloring of their vertices with at most k − 1 colors there is a monochromatic hyperedge. When there is no restriction on the number of the colors used, one can easily avoid monochromatic hyperedges. Then, however, so-called rainbow or multicolored hyperedges might appear. Nešetřil and Rödl [19] called hypergraphs such that in any vertex-coloring there is either a monochromatic or a rainbow hyperedge, selective. They showed an existence of selective r-uniform hypergraphs of girth g for any integers r, g ≥ 2 using probabilistic and explicit constructions. In this paper, we provide a slightly di erent construction of such hypergraphs and summarize the probabilistic approaches. The main building block of the construction, a part-rainbow-forced hypergraph, is of independent interest. This is an r-uniform r-partite hypergraph with a given girth such that in any vertex-coloring that is rainbow on each part, there is a rainbow hyperedge. We give a simple construction of such a hypergraph that does not use iterative amalgamation.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 471-484
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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