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    Wyświetlanie 1-8 z 8
    Tytuł:
    Frequency planning and ramifications of coloring
    Autorzy:
    Eisenblätter, Andreas
    Grötschel, Martin
    Koster, Arie
    Powiązania:
    https://bibliotekanauki.pl/articles/743541.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    frequency assignment
    graph coloring
    Opis:
    This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are T-coloring and list coloring. To model all the subtleties, the techniques of integer programming have proven to be very useful.The ability to produce good frequency plans in practice is essential for the quality of mobile phone networks. The present algorithmic solution methods employ variants of some of the traditional coloring heuristics as well as more sophisticated machinery from mathematical programming. This paper will also address this issue.Finally, this paper discusses several practical frequency assignment problems in detail, states the associated mathematical models, and also points to public electronic libraries of frequency assignment problems from practice. The associated graphs have up to several thousand vertices and range form rather sparse to almost complete.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 51-88
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Coloring rectangular blocks in 3-space
    Autorzy:
    Magnant, Colton
    Martin, Daniel
    Powiązania:
    https://bibliotekanauki.pl/articles/743845.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    chromatic number
    channel assignment problem
    3 dimensional rectangular blocks
    Opis:
    If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 1; 161-170
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On total vertex irregularity strength of graphs
    Autorzy:
    Muthu Guru Packiam, K.
    Kathiresan, Kumarappan
    Powiązania:
    https://bibliotekanauki.pl/articles/743655.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph labeling
    irregularity strength
    total assignment
    vertex irregular total labeling
    Opis:
    Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 1; 39-45
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Linear and cyclic radio k-labelings of trees
    Autorzy:
    Kchikech, Mustapha
    Khennoufa, Riadh
    Togni, Olivier
    Powiązania:
    https://bibliotekanauki.pl/articles/743693.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph theory
    radio channel assignment
    cyclic and linear radio k-labeling
    Opis:
    Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that
    $|f(x)-f(y)| ≥ k+1-d_G(x,y)$,
    for any two distinct vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling. The linear (cyclic, respectively) radio k-labeling number of G is the minimum span of a linear (cyclic, respectively) radio k-labeling of G. In this paper, linear and cyclic radio k-labeling numbers of paths, stars and trees are studied. For the path Pₙ of order n ≤ k+1, we completely determine the cyclic and linear radio k-labeling numbers. For 1 ≤ k ≤ n-2, a new improved lower bound for the linear radio k-labeling number is presented. Moreover, we give the exact value of the linear radio k-labeling number of stars and we present an upper bound for the linear radio k-labeling number of trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 1; 105-123
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Face Irregular Evaluations of Plane Graphs
    Autorzy:
    Bača, Martin
    Ovais, Ali
    Semaničová-Feňovčíková, Andrea
    Suparta, I. Nengah
    Powiązania:
    https://bibliotekanauki.pl/articles/32319469.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    plane graphs
    irregular assignment
    irregularity strength
    face irregular labeling
    face irregularity strength
    Opis:
    We investigate face irregular labelings of plane graphs and we introduce new graph characteristics, namely face irregularity strength of type (α,β,γ). We obtain some estimation on these parameters and determine the precise values for certain families of plane graphs that prove the sharpness of the lower bounds.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 549-568
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radio k-labelings for Cartesian products of graphs
    Autorzy:
    Kchikech, Mustapha
    Khennoufa, Riadh
    Togni, Olivier
    Powiązania:
    https://bibliotekanauki.pl/articles/743543.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph theory
    radio channel assignment
    radio k-labeling
    Cartesian product
    radio number
    antipodal number
    Opis:
    Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that
    $|f(x)-f(y)| ≥ k+1-d_G(x,y)$,
    for any two vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. The radio k-chromatic number is the minimum of max{f(x)-f(y):x,y ∈ V(G)} over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian product of two graphs, providing upper bounds on the radio k-chromatic number for this product. These results help to determine upper and lower bounds for radio k-chromatic numbers of hypercubes and grids. In particular, we show that the ratio of upper and lower bounds of the radio number and the radio antipodal number of the square grid is asymptotically [3/2].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2008, 28, 1; 165-178
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Distance coloring of the hexagonal lattice
    Autorzy:
    Jacko, Peter
    Jendrol', Stanislav
    Powiązania:
    https://bibliotekanauki.pl/articles/744329.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    distance coloring
    distant chromatic number
    hexagonal lattice of the plane
    hexagonal tiling
    hexagonal grid
    radio channel frequency assignment
    Opis:
    Motivated by the frequency assignment problem we study the d-distant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted $χ_d(H)$, is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of $χ_d(H)$ for any d odd and estimations for any d even.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 151-166
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Universality in Graph Properties with Degree Restrictions
    Autorzy:
    Broere, Izak
    Heidema, Johannes
    Mihók, Peter
    Powiązania:
    https://bibliotekanauki.pl/articles/30146518.pdf
    Data publikacji:
    2013-07-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    countable graph
    universal graph
    induced-hereditary
    k-degenerate graph
    graph with colouring number at most k + 1
    graph property with assignment
    Opis:
    Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set ℐc of all countable graphs (since every graph in ℐc is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of ℐc is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 3; 477-492
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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