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    Wyświetlanie 1-14 z 14
    Tytuł:
    Choice-Perfect Graphs
    Autorzy:
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/30146654.pdf
    Data publikacji:
    2013-03-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph coloring
    list coloring
    choice-perfect graph
    Opis:
    Given a graph $ G = (V,E) $ and a set $ L_v $ of admissible colors for each vertex $ v \in V $ (termed the list at $v$), a list coloring of $G$ is a (proper) vertex coloring $ \phi : V \rightarrow \bigcup \text{}_{v \in V} L_v $ such that $ \phi (v) \in L_v $ for all $ v \in V $ and $ \phi(u) \ne \phi(v) $ for all $ uv \in E $. If such a $ \phi $ exists, $G$ is said to be list colorable. The choice number of $G$ is the smallest natural number $k$ for which $G$ is list colorable whenever each list contains at least $k$ colors. In this note we initiate the study of graphs in which the choice number equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, respectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 1; 231-242
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized colorings and avoidable orientations
    Autorzy:
    Szigeti, Jenő
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/971967.pdf
    Data publikacji:
    1997
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hereditary property
    graph coloring
    Opis:
    Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family of k+3 directed graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1997, 17, 1; 137-145
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dominating bipartite subgraphs in graphs
    Autorzy:
    Bacsó, Gábor
    Michalak, Danuta
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/744313.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    dominating set
    dominating subgraph
    forbidden induced subgraph
    bipartite graph
    k-partite graph
    Opis:
    A graph G is hereditarily dominated by a class of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to . In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 85-94
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Highly connected counterexamples to a conjecture on α-domination
    Autorzy:
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/744177.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    dominating set
    α-domination
    Opis:
    An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 3; 435-440
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Decompositions of Plane Graphs Under Parity Constrains Given by Faces
    Autorzy:
    Czap, Július
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/30146456.pdf
    Data publikacji:
    2013-07-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    plane graph
    parity partition
    edge coloring
    Opis:
    An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 3; 521-530
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Domination in partitioned graphs
    Autorzy:
    Tuza, Zsolt
    Vestergaard, Preben
    Powiązania:
    https://bibliotekanauki.pl/articles/743565.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    dominating set
    domination number
    vertex partition
    Opis:
    Let V₁, V₂ be a partition of the vertex set in a graph G, and let $γ_i$ denote the least number of vertices needed in G to dominate $V_i$. We prove that γ₁+γ₂ ≤ [4/5]|V(G)| for any graph without isolated vertices or edges, and that equality occurs precisely if G consists of disjoint 5-paths and edges between their centers. We also give upper and lower bounds on γ₁+γ₂ for graphs with minimum valency δ, and conjecture that γ₁+γ₂ ≤ [4/(δ+3)]|V(G)| for δ ≤ 5. As δ gets large, however, the largest possible value of (γ₁+γ₂)/|V(G)| is shown to grow with the order of (logδ)/(δ).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 199-210
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Grundy Total Domination Number in Product Graphs
    Autorzy:
    Brešar, Boštjan
    Bujtás, Csilla
    Gologranc, Tanja
    Klavžar, Sandi
    Košmrlj, Gašper
    Marc, Tilen
    Patkós, Balázs
    Tuza, Zsolt
    Vizer, Máté
    Powiązania:
    https://bibliotekanauki.pl/articles/32083828.pdf
    Data publikacji:
    2021-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total domination
    Grundy total domination number
    graph product
    Opis:
    A longest sequence $(v_1, . . ., v_k)$ of vertices of a graph $G$ is a Grundy total dominating sequence of $G$ if for all $i$, \(N(υ_i)\backslash\bigcup_{j=1}^{i-1}N(υ_j)≠∅\). The length $k$ of the sequence is called the Grundy total domination number of $G$ and denoted $\gamma_{gr}^t(G)$. In this paper, the Grundy total domination number is studied on four standard graph products. For the direct product we show that $\gamma_{gr}^t(G×H)≥\gamma_{gr}^t(G)\gamma_{gr}^t(H)$, conjecture that the equality always holds, and prove the conjecture in several special cases. For the lexicographic product we express $\gamma_{gr}^t(G∘H)$ in terms of related invariant of the factors and find some explicit formulas for it. For the strong product, lower bounds on $\gamma_{gr}^t(G⊠H)$ are proved as well as upper bounds for products of paths and cycles. For the Cartesian product we prove lower and upper bounds on the Grundy total domination number when factors are paths or cycles.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 1; 225-247
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    3-consecutive c-colorings of graphs
    Autorzy:
    Bujtás, Csilla
    Sampathkumar, E.
    Tuza, Zsolt
    Subramanya, M.
    Dominic, Charles
    Powiązania:
    https://bibliotekanauki.pl/articles/744032.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph coloring
    vertex coloring
    consecutive coloring
    upper chromatic number
    Opis:
    A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number $(χ̅)_{3CC}(G)$ of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with $(χ̅)_{3CC}(G) ≥ k$ for k = 3 and k = 4.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 3; 393-405
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The cost chromatic number and hypergraph parameters
    Autorzy:
    Bacsó, Gábor
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/743998.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph coloring
    cost chromatic number
    intersection number of a hypergraph
    Opis:
    In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2006, 26, 3; 369-376
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graphs without induced P₅ and C₅
    Autorzy:
    Bacsó, Gabor
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/744580.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph domination
    connected domination
    complete subgraph
    forbidden induced subgraph
    characterization
    Opis:
    Zverovich [Discuss. Math. Graph Theory 23 (2003), 159-162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P₅ and C₅. Here we show (with an independent proof) that the following stronger result is also valid: Every P₅-free and C₅-free connected graph contains a minimum-size dominating set that induces a complete subgraph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2004, 24, 3; 503-507
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    ℤ2 × ℤ2 -Cordial Cycle-Free Hypergraphs
    Autorzy:
    Cichacz, Sylwia
    Görlich, Agnieszka
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/32361757.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    V 4 -cordial graph
    hypergraph
    labeling of hypergraph
    hyper-tree
    Opis:
    Hovey introduced A-cordial labelings as a generalization of cordial and harmonious labelings [7]. If A is an Abelian group, then a labeling f : V (G) → A of the vertices of some graph G induces an edge labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. The problem of A-cordial labelings of graphs can be naturally extended for hypergraphs. It was shown that not every 2-uniform hypertree (i.e., tree) admits a ℤ2 × ℤ2-cordial labeling [8]. The situation changes if we consider p-uniform hypertrees for a bigger p. We prove that a p-uniform hypertree is ℤ2 × ℤ2-cordial for any p > 2, and so is every path hypergraph in which all edges have size at least 3. The property is not valid universally in the class of hypergraphs of maximum degree 1, for which we provide a necessary and sufficient condition.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1021-1040
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graph domination in distance two
    Autorzy:
    Bacsó, Gábor
    Tálos, Attila
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/744316.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    dominating set
    connected domination
    distance domination
    forbidden induced subgraph
    Opis:
    Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that $Dom Dom _u = Dom₂ _u$ holds for $_u$ = {all connected graphs without induced $P_u$} (u ≥ 2). (In particular, ₂ = {K₁} and ₃ = {all complete graphs}.) Some negative examples are also given.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 121-128
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graph colorings with local constraints - a survey
    Autorzy:
    Tuza, Zsolt
    Powiązania:
    https://bibliotekanauki.pl/articles/972031.pdf
    Data publikacji:
    1997
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph coloring
    list coloring
    choice number
    precoloring extension
    complexity of algorithms
    chromatic number
    Opis:
    We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered.
    In one of the most general formulations, a graph G = (V,E), sets L(v) of admissible colors, and natural numbers $c_v$ for the vertices v ∈ V are given, and the question is whether there can be chosen a subset C(v) ⊆ L(v) of cardinality $c_v$ for each vertex in such a way that the sets C(v),C(v') are disjoint for each pair v,v' of adjacent vertices. The particular case of constant |L(v)| with $c_v$ = 1 for all v ∈ V leads to the concept of choice number, a graph parameter showing unexpectedly different behavior compared to the chromatic number, despite these two invariants have nearly the same value for almost all graphs.
    To illustrate typical techniques, some of the proofs are sketched.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1997, 17, 2; 161-228
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Color-bounded hypergraphs, V: host graphs and subdivisions
    Autorzy:
    Bujtás, Csilla
    Tuza, Zsolt
    Voloshin, Vitaly
    Powiązania:
    https://bibliotekanauki.pl/articles/743863.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed hypergraph
    color-bounded hypergraph
    vertex coloring
    arboreal hypergraph
    hypertree
    feasible set
    host graph
    edge subdivision
    Opis:
    A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set = {E₁,...,Eₘ}, together with integers $s_i$ and $t_i$ satisfying $1 ≤ s_i ≤ t_i ≤ |E_i|$ for each i = 1,...,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge $E_i$ satisfies $s_i ≤ |φ(E_i)| ≤ t_i$. The hypergraph ℋ is colorable if it admits at least one proper coloring.
    We consider hypergraphs ℋ over a "host graph", that means a graph G on the same vertex set X as ℋ, such that each $E_i$ induces a connected subgraph in G. In the current setting we fix a graph or multigraph G₀, and assume that the host graph G is obtained by some sequence of edge subdivisions, starting from G₀.
    The colorability problem is known to be NP-complete in general, and also when restricted to 3-uniform "mixed hypergraphs", i.e., color-bounded hypergraphs in which $|E_i| = 3$ and $1 ≤ s_i ≤ 2 ≤ t_i ≤ 3$ holds for all i ≤ m. We prove that for every fixed graph G₀ and natural number r, colorability is decidable in polynomial time over the class of r-uniform hypergraphs (and more generally of hypergraphs with $|E_i| ≤ r$ for all 1 ≤ i ≤ m) having a host graph G obtained from G₀ by edge subdivisions. Stronger bounds are derived for hypergraphs for which G₀ is a tree.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 223-238
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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