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    Wyświetlanie 1-15 z 15
    Tytuł:
    Relations between the domination parameters and the chromatic index of a graph
    Autorzy:
    Ulatowski, Włodzimierz
    Powiązania:
    https://bibliotekanauki.pl/articles/744471.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    domination parameters
    chromatic index
    Opis:
    In this paper we show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality holds.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 3; 615-627
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the ρ-Edge Stability Number of Graphs
    Autorzy:
    Kemnitz, Arnfried
    Marangio, Massimiliano
    Powiązania:
    https://bibliotekanauki.pl/articles/32361738.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge stability number
    line stability
    invariant
    chromatic edge stability index
    chromatic index
    edge coloring
    Opis:
    For an arbitrary invariant $ \rho(G) $ of a graph $G$ the $ \rho $-edge stability number $ es_\rho (G) $ is the minimum number of edges of $G$ whose removal results in a graph $ H \subseteq G $ with $ \rho (H) \ne \rho (G) $ or with $ E(H) = \emptyset $. In the first part of this paper we give some general lower and upper bounds for the $ \rho $-edge stability number. In the second part we study the $ \chi^' $-edge stability number of graphs, where $ \chi^' = \chi^' (G) $ is the chromatic index of $G$. We prove some general results for the so-called chromatic edge stability index $ es_{ \chi^′ } (G) $ and determine $ es_{ \chi^′ } (G) $ exactly for specific classes of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 249-262
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper Bounds for the Strong Chromatic Index of Halin Graphs
    Autorzy:
    Hu, Ziyu
    Lih, Ko-Wei
    Liu, Daphne Der-Fen
    Powiązania:
    https://bibliotekanauki.pl/articles/16647759.pdf
    Data publikacji:
    2018-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    strong edge-coloring
    strong chromatic index
    Halin graphs
    Opis:
    The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph G by drawing T on the plane and then drawing a cycle C connecting all its leaves in such a way that C forms the boundary of the unbounded face. We call T the characteristic tree of G. Let G denote a Halin graph with maximum degree Δ and characteristic tree T. We prove that χ′s(G) ⩽ 2Δ + 1 when Δ ⩾ 4. In addition, we show that if Δ = 4 and G is not a wheel, then χ′s(G) ⩽ χ′s(T) + 2. A similar result for Δ = 3 was established by Lih and Liu [21].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 1; 5-26
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper Bounds for the Strong Chromatic Index of Halin Graphs
    Autorzy:
    Hu, Ziyu
    Lih, Ko-Wei
    Liu, Daphne Der-Fen
    Powiązania:
    https://bibliotekanauki.pl/articles/31342445.pdf
    Data publikacji:
    2018-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    strong edge-coloring
    strong chromatic index
    Halin graphs
    Opis:
    The strong chromatic index of a graph $G$, denoted by $ \chi_s^′ (G) $, is the minimum number of vertex induced matchings needed to partition the edge set of $G$. Let $T$ be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph $G$ by drawing $T$ on the plane and then drawing a cycle $C$ connecting all its leaves in such a way that $C$ forms the boundary of the unbounded face. We call $T$ the characteristic tree of $G$. Let $G$ denote a Halin graph with maximum degree $ \Delta $ and characteristic tree $T$. We prove that $ \chi_s^′ (G) \le 2 \Delta + 1 $ when $ \Delta \ge 4 $. In addition, we show that if $ \Delta = 4 $ and $G$ is not a wheel, then $ \chi_s^′ (G) \le \chi_s^′ (T) + 2 $. A similar result for $ \Delta = 3 $ was established by Lih and Liu [21].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 1; 5-26
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some maximum multigraphs and edge/vertex distance colourings
    Autorzy:
    Skupień, Zdzisław
    Powiązania:
    https://bibliotekanauki.pl/articles/971931.pdf
    Data publikacji:
    1995
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    (strong) chromatic index
    chromatic number
    matching
    hypercube
    error-correcting code
    asymptotics
    Opis:
    Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1995, 15, 1; 89-106
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On locally irregular decompositions of subcubic graphs
    Autorzy:
    Baudon, O.
    Bensmail, J.
    Hocquard, H.
    Senhaji, M.
    Sopena, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/254905.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    locally irregular edge-colouring irregular chromatic index
    subcubic graphs
    Opis:
    A graph G is locally irregular if every two adjacent vertices of G have different degrees. A locally irregular decomposition of G is a partition E1,.. . , Ek of E(G) such that each G[Ei] is locally irregular. Not all graphs admit locally irregular decompositions, but for those who are decomposable, in that sense, it was conjectured by Baudon, Bensmail, Przybyło and Woźniak that they decompose into at most 3 locally irregular graphs. Towards that conjecture, it was recently proved by Bensmail, Merker and Thomassen that every decomposable graph decomposes into at most 328 locally irregular graphs. We here focus on locally irregular decompositions of subcubic graphs, which form an important family of graphs in this context, as all non-decomposable graphs are subcubic. As a main result, we prove that decomposable subcubic graphs decompose into at most 5 locally irregular graphs, and only at most 4 when the maximum average degree is less than 12/5. We then consider weaker decompositions, where subgraphs can also include regular connected components, and prove the relaxations of the conjecture above for subcubic graphs.
    Źródło:
    Opuscula Mathematica; 2018, 38, 6; 795-817
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Proper (Strong) Rainbow Connection of Graphs
    Autorzy:
    Jiang, Hui
    Li, Wenjing
    Li, Xueliang
    Magnant, Colton
    Powiązania:
    https://bibliotekanauki.pl/articles/32083886.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    proper (strong) rainbow connection number
    Cartesian product
    chromatic index
    Opis:
    A path in an edge-colored graph $G$ is called a rainbow path if no two edges on the path have the same color. The graph $G$ is called rainbow connected if between every pair of distinct vertices of $G$, there is a rainbow path. Recently, Johnson et al. considered this concept with the additional requirement that the coloring of $G$ is proper. The proper rainbow connection number of $G$, denoted by $prc(G)$, is the minimum number of colors needed to properly color the edges of $G$ so that $G$ is rainbow connected. Similarly, the proper strong rainbow connection number of $G$, denoted by $psrc(G)$, is the minimum number of colors needed to properly color the edges of $G$ such that for any two distinct vertices of $G$, there is a rainbow geodesic (shortest path) connecting them. In this paper, we characterize those graphs with proper rainbow connection numbers equal to the size or within 1 of the size. Moreover, we completely solve a question proposed by Johnson et al. by proving that if \(G = K_{p1} \Box \dots \Box K_{pn}\), where $n≥ 1$, and $p_1, . . ., p_n>1$ are integers, then $prc(G) = psrc(G) = χ^′(G)$, where $χ^′(G)$ denotes the chromatic index of $G$. Finally, we investigate some suffcient conditions for a graph $G$ to satisfy $prc(G) = rc(G)$, and make some slightly positive progress by using a relation between $rc(G)$ and the girth of the graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 469-479
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Localization of jumps of the point-distinguishing chromatic index of $K_{n,n}
    Autorzy:
    Horňák, Mirko
    Soták, Roman
    Powiązania:
    https://bibliotekanauki.pl/articles/972023.pdf
    Data publikacji:
    1997
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Point-distinguishing chromatic index
    colour set
    complete equibipartite graph
    Opis:
    The point-distinguishing chromatic index of a graph represents the minimum number of colours in its edge colouring such that each vertex is distinguished by the set of colours of edges incident with it. Asymptotic information on jumps of the point-distinguishing chromatic index of $K_{n,n}$ is found.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1997, 17, 2; 243-251
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Star Chromatic Index of Generalized Petersen Graphs
    Autorzy:
    Zhu, Enqiang
    Shao, Zehui
    Powiązania:
    https://bibliotekanauki.pl/articles/32083878.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    star edge-coloring
    star chromatic index
    generalized Petersen graph
    Opis:
    The star $k$-edge-coloring of graph $G$ is a proper edge coloring using $k$ colors such that no path or cycle of length four is bichromatic. The minimum number $k$ for which $G$ admits a star $k$-edge-coloring is called the star chromatic index of $G$, denoted by $χ_s^′(G)$. Let $GCD(n, k)$ be the greatest common divisor of $n$ and $k$. In this paper, we give a necessary and sufficient condition of $χ_s^′(P(n, k)) = 4$ for a generalized Petersen graph $P(n, k)$ and show that “almost all” generalized Petersen graphs have a star 5-edge-colorings. Furthermore, for any two integers $k$ and $n(≥2k + 1)$ such that $GCD(n, k) ≥ 3, P (n, k)$ has a star 5-edge-coloring, with the exception of the case that $GCD(n, k) = 3$, $k ≠ GCD(n, k)$ and \(\frac{n}{3}≡1(mod3)\).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 427-439
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Edge colorings and total colorings of integer distance graphs
    Autorzy:
    Kemnitz, Arnfried
    Marangio, Massimiliano
    Powiązania:
    https://bibliotekanauki.pl/articles/743555.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integer distance graph
    chromatic number
    choice number
    chromatic index
    choice index
    total chromatic number
    total choice number
    Opis:
    An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 149-158
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle
    Autorzy:
    Frigerio, Laura
    Lastaria, Federico
    Salvi, Norma
    Powiązania:
    https://bibliotekanauki.pl/articles/743981.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    chromatic index
    adjacent vertex distinguishing edge coloring
    direct product
    matching
    Opis:
    In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 3; 547-557
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vertex-distinguishing edge-colorings of linear forests
    Autorzy:
    Cichacz, Sylwia
    Przybyło, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/744522.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    irregular edge-coloring
    vertex-distinguishing edge-coloring
    point-distinguishing chromatic index
    Opis:
    In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 1; 95-103
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong Edge-Coloring Of Planar Graphs
    Autorzy:
    Song, Wen-Yao
    Miao, Lian-Ying
    Powiązania:
    https://bibliotekanauki.pl/articles/31341618.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    strong edge-coloring
    strong chromatic index
    planar graph
    dis- charging method
    Opis:
    A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by $ \chi_s^' (G) $ the strong chromatic index of $G$ which is the smallest integer $k$ such that $G$ can be strongly edge-colored with $k$ colors. It is known that every planar graph $G$ has a strong edge-coloring with at most $ 4 \Delta (G) + 4 $ colors [R.J. Faudree, A. Gyárfás, R.H. Schelp and Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211]. In this paper, we show that if $G$ is a planar graph with $ g \ge 5$, then $ \chi_s^' (G) \le 4 \Delta (G) − 2 $ when $ \Delta (G) \ge 6 $ and $ \chi_s^' (G) \le 19 $ when $ \Delta (G) = 5 $, where $g$ is the girth of $G$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 845-857
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Three edge-coloring conjectures
    Autorzy:
    Schelp, Richard
    Powiązania:
    https://bibliotekanauki.pl/articles/743559.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge-coloring
    Ramsey number
    vertex-distinguishing edge-coloring
    strong chromatic index
    balanced edge-coloring
    local coloring
    mean coloring
    Opis:
    The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 173-182
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    General multiplicative Zagreb indices of graphs with given clique number
    Autorzy:
    Vetrik, Tomas
    Balachandran, Selvaraj
    Powiązania:
    https://bibliotekanauki.pl/articles/255259.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    clique number
    multiplicative Zagreb index
    chromatic number
    Opis:
    We obtain lower and upper bounds on general multiplicative Zagreb indices for graphs of given clique number and order. Bounds on the basic multiplicative Zagreb indices and on the multiplicative sum Zagreb index follow from our results. We also determine graphs with the smallest and the largest indices.
    Źródło:
    Opuscula Mathematica; 2019, 39, 3; 433-446
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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