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Tytuł:
A note on M2-edge colorings of graphs
Autorzy:
Czap, J.
Powiązania:
https://bibliotekanauki.pl/articles/255532.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
edge colouring
graph
Opis:
An edge coloring φ of a graph G is called an M2-edge coloring if [formula] every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let K2(G) denote the maximum number of colors used in an M2-edge coloring of G. Let G1, G2 and G3 be graphs such that G1 ⊆ G2 ⊆ G3. In this paper we deal with the following question: Assuming that K2(G1) = K2(G3), does it hold K2(G1) = K2(G2) = K2(G3)?
Źródło:
Opuscula Mathematica; 2015, 35, 3; 287-291
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
A note on the vertex-distinguishing index for some cubic graphs
Autorzy:
Taczuk, K.
Woźniak, M.
Powiązania:
https://bibliotekanauki.pl/articles/2050799.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
edge colouring
vertex-distinguishing colouring
cubic graphs
Opis:
The vertex-distinguishing index of a graph G (vdi (G)) is the minimum number of colours required to colour properly the edges of a graph in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some families of cubic graphs.
Źródło:
Opuscula Mathematica; 2004, 24, 2; 223-229
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
On Fibonacci numbers in edge coloured trees
Autorzy:
Bednarz, U.
Bród, D.
Szynal-Liana, A.
Włoch, I.
Wołowiec-Musiał, M.
Powiązania:
https://bibliotekanauki.pl/articles/254765.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
edge colouring
tree
tripod
Fibonacci numbers
Opis:
In this paper we show the applications of the Fibonacci numbers in edge coloured trees. We determine the second smallest number of all (A, 2B)-edge colourings in trees. We characterize the minimum tree achieving this second smallest value.
Źródło:
Opuscula Mathematica; 2017, 37, 4; 479-490
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
Note about sequences of extrema \((A,2B)\)-edge coloured trees
Autorzy:
Bednarz, Urszula
Włoch, Iwona
Powiązania:
https://bibliotekanauki.pl/articles/747039.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Edge colouring
trees
Fibonacci numbers
telephone numbers
Opis:
In this paper we determine successive extremal trees with respect to the number of all \((A,2B)\)-edge colourings.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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 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 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 1-15 z 16

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