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    Wyświetlanie 1-10 z 10
    Tytuł:
    Graphs with rainbow connection number two
    Autorzy:
    Kemnitz, Arnfried
    Schiermeyer, Ingo
    Powiązania:
    https://bibliotekanauki.pl/articles/743883.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge colouring
    rainbow colouring
    rainbow connection
    Opis:
    An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n and size m, where $\binom{n-1}{2} + 1 ≤ m ≤ \binom{n}{2} - 1$. We also characterize graphs with rainbow connection number two and large clique number.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 313-320
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Palette Index of Complete Bipartite Graphs
    Autorzy:
    Horňák, Mirko
    Hudák, Juraj
    Powiązania:
    https://bibliotekanauki.pl/articles/31342323.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge colouring
    palette index
    bipartite graph
    Opis:
    The palette of a vertex x of a graph G determined by a proper edge colouring φ of G is the set {φ(xy) : xy ∈ E(G)} and the diversity of φ is the number of different palettes determined by φ. The palette index of G is the minimum of diversities of φ taken over all proper edge colourings φ of G. In the article we determine the palette index of Km,n for m ≤ 5 and pose two conjectures concerning the palette index of complete bipartite graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 463-476
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On generating snarks
    Autorzy:
    Chisala, Busiso
    Powiązania:
    https://bibliotekanauki.pl/articles/744213.pdf
    Data publikacji:
    1998
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    snarks
    cubic graphs
    sirth
    edge colouring
    Opis:
    We discuss the construction of snarks (that is, cyclically 4-edge connected cubic graphs of girth at least five which are not 3-edge colourable) by using what we call colourable snark units and a welding process.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1998, 18, 2; 147-158
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fibonacci and Telephone Numbers in Extremal Trees
    Autorzy:
    Bednarz, Urszula
    Włoch, Iwona
    Powiązania:
    https://bibliotekanauki.pl/articles/31342435.pdf
    Data publikacji:
    2018-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge colouring
    tripod
    Fibonacci numbers
    telephone numbers
    Opis:
    In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 1; 121-133
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
    Autorzy:
    Borowiecka-Olszewska, Marta
    Drgas-Burchardt, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/31341980.pdf
    Data publikacji:
    2017-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge colouring
    consecutive (interval) colouring
    deficiency
    Sevastjanov graph
    forbidden graph
    Opis:
    A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 2; 315-336
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On odd and semi-odd linear partitions of cubic graphs
    Autorzy:
    Fouquet, Jean-Luc
    Thuillier, Henri
    Vanherpe, Jean-Marie
    Wojda, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/743181.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cubic graph
    linear arboricity
    strong matching
    edge-colouring
    Opis:
    A linear forest is a graph whose connected components are chordless paths. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition.
    In this paper we consider linear partitions of cubic simple graphs for which it is well known that la(G) = 2. A linear partition $L = (L_B,L_R)$ is said to be odd whenever each path of $L_B ∪ L_R$ has odd length and semi-odd whenever each path of $L_B$ (or each path of $L_R$) has odd length.
    In [2] Aldred and Wormald showed that a cubic graph G is 3-edge colourable if and only if G has an odd linear partition. We give here more precise results and we study moreover relationships between semi-odd linear partitions and perfect matchings.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 2; 275-292
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On k-intersection edge colourings
    Autorzy:
    Muthu, Rahul
    Narayanan, N.
    Subramanian, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/744421.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph theory
    k-intersection edge colouring
    probabilistic method
    Opis:
    We propose the following problem. For some k ≥ 1, a graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the k-intersection chromatic index and is denoted χ'ₖ(G). Let fₖ be defined by
    $fₖ(Δ) = max_{G : Δ(G) = Δ} {χ'ₖ(G)}$.
    We show that fₖ(Δ) = Θ(Δ²/k). We also discuss some open problems.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 2; 411-418
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Critical and Flow-Critical Snarks Coincide
    Autorzy:
    Máčajová, Edita
    Škoviera, Martin
    Powiązania:
    https://bibliotekanauki.pl/articles/32083890.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    nowhere-zero flow
    edge-colouring
    cubic graph
    snark
    Opis:
    Over the past twenty years, critical and bicritical snarks have been appearing in the literature in various forms and in different contexts. Two main variants of criticality of snarks have been studied: criticality with respect to the non-existence of a 3-edge-colouring and criticality with respect to the non-existence of a nowhere-zero 4-flow. In this paper we show that these two kinds of criticality coincide, thereby completing previous partial results of de Freitas et al. [Electron. Notes Discrete Math. 50 (2015) 199–204] and Fiol et al. [Electron. J. Combin. 25 (2017) #P4.54].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 503-511
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Small Balanceable, Strongly-Balanceable and Omnitonal Graphs
    Autorzy:
    Caro, Yair
    Lauri, Josef
    Zarb, Christina
    Powiązania:
    https://bibliotekanauki.pl/articles/32222540.pdf
    Data publikacji:
    2022-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge-colouring
    zero-sum Ramsey
    balanceable graphs
    omnitonal graphs
    Opis:
    In Ramsey Theory for graphs we are given a graph G and we are required to find the least n0 such that, for any n ≥ n0, any red/blue colouring of the edges of Kn gives a subgraph G all of whose edges are blue or all are red. Here we shall be requiring that, for any red/blue colouring of the edges of Kn, there must be a copy of G such that its edges are partitioned equally as red or blue (or the sizes of the colour classes differs by one in the case when G has an odd number of edges). This introduces the notion of balanceable graphs and the balance number of G which, if it exists, is the minimum integer bal(n, G) such that, for any red/blue colouring of E(Kn) with more than bal(n, G) edges of either colour, Kn will contain a balanced coloured copy of G as described above. The strong balance number sbal(n, G) is analogously defined when G has an odd number of edges, but in this case we require that there are copies of G with both one more red edge and one more blue edge. These parameters were introduced by Caro, Hansberg and Montejano. These authors also introduce the more general omnitonal number ot(n, G) which requires copies of G containing a complete distribution of the number of red and blue edges over E(G). In this paper we shall catalogue bal(n, G), sbal(n, G) and ot(n, G) for all graphs G on at most four edges. We shall be using some of the key results of Caro et al. which we here reproduce in full, as well as some new results which we prove here. For example, we shall prove that the union of two bipartite graphs with the same number of edges is always balanceable.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1219-1235
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Proper Rainbow Connection Number of Graphs
    Autorzy:
    Doan, Trung Duy
    Schiermeyer, Ingo
    Powiązania:
    https://bibliotekanauki.pl/articles/32222687.pdf
    Data publikacji:
    2021-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge-colouring
    rainbow connection number
    proper rainbow connection number
    Opis:
    A path in an edge-coloured graph is called a rainbow path if its edges receive pairwise distinct colours. An edge-coloured graph is said to be rainbow connected if any two distinct vertices of the graph are connected by a rainbow path. The minimum k for which there exists such an edge-colouring is the rainbow connection number rc(G) of G. Recently, Bau et al. [Rainbow connectivity in some Cayley graphs, Australas. J. Combin. 71 (2018) 381–393] introduced this concept with the additional requirement that the edge-colouring must be proper. The proper rainbow connection number of G, denoted by prc(G), is the minimum number of colours needed in order to make it properly rainbow connected. Obviously, prc(G) ≥ max{rc(G), χ′(G)}. In this paper we first prove an improved upper bound prc(G) ≤ n for every connected graph G of order n ≥ 3. Next we show that the difference prc(G) – max{rc(G), χ′(G)} can be arbitrarily large. Finally, we present several sufficient conditions for graph classes satisfying prc(G) = χ′(G).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 3; 809-826
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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