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Wyniki wyszukiwania dla: GRUNDY NUMBER

  • Minimum order of graphs with given coloring parameters

    Publikacja

    - DISCRETE MATHEMATICS - 2015

    A complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...

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  • New potential functions for greedy independence and coloring

    Publikacja

    A potential function $f_G$ of a finite, simple and undirected graph $G=(V,E)$ is an arbitrary function $f_G : V(G) \rightarrow \mathbb{N}_0$ that assigns a nonnegative integer to every vertex of a graph $G$. In this paper we define the iterative process of computing the step potential function $q_G$ such that $q_G(v)\leq d_G(v)$ for all $v\in V(G)$. We use this function in the development of new Caro-Wei-type and Brooks-type...

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  • Dynamic coloring of graphs

    Publikacja

    - FUNDAMENTA INFORMATICAE - 2012

    Dynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...

  • Dynamic F-free Coloring of Graphs

    Publikacja

    - GRAPHS AND COMBINATORICS - 2018

    A problem of graph F-free coloring consists in partitioning the vertex set of a graph such that none of the resulting sets induces a graph containing a fixed graph F as an induced subgraph. In this paper we consider dynamic F-free coloring in which, similarly as in online coloring, the graph to be colored is not known in advance; it is gradually revealed to the coloring algorithm that has to color each vertex upon request as well...

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  • Computational aspects of greedy partitioning of graphs

    In this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...

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  • On Computational Aspects of Greedy Partitioning of Graphs

    Publikacja

    - 2017

    In this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...

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  • Jerzy Kowalski dr hab. inż.

  • Total Domination Versus Domination in Cubic Graphs

    A dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...

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  • On some Zarankiewicz numbers and bipartite Ramsey Numbers for Quadrilateral

    Publikacja

    - ARS COMBINATORIA - 2015

    The Zarankiewicz number z ( m, n ; s, t ) is the maximum number of edges in a subgraph of K m,n that does not contain K s,t as a subgraph. The bipartite Ramsey number b ( n 1 , · · · , n k ) is the least positive integer b such that any coloring of the edges of K b,b with k colors will result in a monochromatic copy of K n i ,n i in the i -th color, for some i , 1 ≤ i ≤ k . If n i = m for all i , then we denote this number by b k ( m )....

  • New Proofs of Some Fibonacci Identities

    Publikacja

    Lucas proved in 1876 several identities for Fibonacci numbers. We give elementary and short proofs of them.

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  • On domination multisubdivision number of unicyclic graphs

    Publikacja

    The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...

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  • Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number

    Publikacja

    - FUNDAMENTA INFORMATICAE - 2017

    A vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...

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  • The Backbone Coloring Problem for Bipartite Backbones

    Let G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...

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  • Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected

    Let f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...

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  • On trees with double domination number equal to 2-domination number plus one

    A vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...

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  • On trees with double domination number equal to total domination number plus one

    Publikacja

    A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...

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  • Jakub Miler dr inż.

    Kariera akademicka: 2000: mgr inż. Wydział ETI, Politechnika Gdańska, praca pt. "Computer system for supporting risk management in a software engineering project", promotor prof. Janusz Górski 2005: dr inż. Wydział ETI, Politechnika Gdańska, rozprawa pt. "A Method of Software Project Risk Identification and Analysis", obroniona z wyróżnieniem, dziedzina nauki techniczne, dyscyplina informatyka, promotor prof. Janusz Górski Zainteresowania...

  • Bondage number of grid graphs

    The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.

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  • Navier number and transition to turbulence

    The motivation behind this article is to explain a role of the Navier number (Na -dimensionless slip-length) in prediction of closures for laminar to turbulent transition undergoing via eddies detachment from the slip layer in nano-cannals. Additionally the role of the Navier number Na in universal modeling of phenomenon of enhanced mass flow rate reported in micro- and nano-channels has been explained. The Na number should be...

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  • The paired-domination and the upper paired-domination numbers of graphs

    Publikacja

    In this paper we obtain the upper bound for the upper paired-domination number and we determine the extremal graphs achieving this bound. Moreover we determine the upper paired- domination number for cycles.

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  • Jacek Namieśnik prof. dr hab. inż.

    Osoby

    Urodził się 10 grudnia 1949 r. w Mogilnie. Prof. Jacek Namieśnik to specjalista z zakresu chemii analitycznej i chemii środowiska, głównie nowych rozwiązań aparaturowych i metodycznych w zakresie przygotowania próbek do analizy. Autor lub współautor ponad 800 prac opublikowanych w czasopismach z listy JCR oraz około 200 prac, które ukazały się w innych czasopismach. Prace znajdujące się w dorobku prof. Jacka Namieśnika cieszą się...

  • On trees with double domination number equal to 2-outer-independent domination number plus one

    A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...

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  • Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective

    Publikacja

    - TOPOLOGY AND ITS APPLICATIONS - 2012

    Let f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...

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  • The convex domination subdivision number of a graph

    Publikacja

    Let G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...

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  • A NOTE ON ON-LINE RAMSEY NUMBERS FOR QUADRILATERALS

    Publikacja

    - Opuscula Mathematica - 2014

    We consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder’s goal is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \widetilde{r}(H) of...

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  • A survey on known values and bounds on the Shannon capacity

    Publikacja

    - 2014

    In this survey we present exact values and bounds on the Shannon capacity for different classes of graphs, for example for regular graphs and Kneser graphs. Additionally, we show a relation between Ramsey numbers and Shannon capacity.

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  • On the doubly connected domination number of a graph

    Publikacja

    - Central European Journal of Mathematics - 2006

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  • On the total restrained domination number of a graph

    W pracy przedstawione są ograniczenia i własności liczby dominowania podwójnie totalnego.

  • The outer-connected domination number of a graph

    Publikacja

    W pracy została zdefiniowana liczba dominowania zewnętrznie spójnego i przedstawiono jej podstawowe własności.

  • Coronas and Domination Subdivision Number of a Graph

    In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.

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  • TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH

    Publikacja

    - Discussiones Mathematicae Graph Theory - 2015

    The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...

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  • Lower bound on the domination number of a tree.

    Publikacja

    - 2004

    W pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.

  • On the doubly connected domination number of a graph

    W pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.

  • Unicyclic graphs with equal total and total outer-connected domination numbers

    Publikacja

    Let G = (V,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a total dominating set if D is dominating and the in- duced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total domi- nating set of G. A set D ⊆ V (G) is a total outer–connected dominating set if D is total dominating and the induced subgraph G[V (G)−D] is a connected graph. The total outer–connected...

  • On configuration of residue scaling process in pipelined radix-4 MQRNS FFT processor

    Residue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and outputs four complex residue numbers. In order to prevent the arithmetic overflow in the succesive stage, every number has to be scaled,...

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  • Lower bound on the paired domination number of a tree

    W pracy przedstawione jest ograniczenie dolne dla liczby dominowania parami oraz scharakteryzowane są wszystkie drzewa ekstremalne.

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  • Non-standard binary weighted number systems

    Publikacja

    - 2006

    Zdefiniowano szeroką klasę binarnych systemów wagowych. Wszystkie sa wzajemnie jednoznaczne ale mogą być zupełne lub niezupełne. Jeżeli wagi systemu są kolejnymi liczbami naturalnymi to system jest minimalny.Jesli wagi sa kolejnymi potęgami podstawy Z to system jest maksymalny. W przestrzeni między tymi systemami znajdują się inne systemy binarne. Kilka z nich przedstawiono w referacie.

  • Entanglement and Nonlocality are Inequivalent for Any Number of Parties

    Publikacja

    - PHYSICAL REVIEW LETTERS - 2015

    Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite...

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  • T-colorings, divisibility and circular chromatic number

    Let T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...

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  • Weakly convex domination subdivision number of a graph

    Publikacja

    - FILOMAT - 2016

    A set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...

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  • Bounds on the vertex-edge domination number of a tree

    Publikacja

    - COMPTES RENDUS MATHEMATIQUE - 2014

    A vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...

  • Influence of edge subdivision on the convex domination number

    We study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.

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  • Graphs with convex domination number close to their order

    Publikacja

    W pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.

  • All graphs with restrained domination number three less than their order

    W pracy opisana jest rodzina wszystkich grafów, dla których liczbadominowania zewnętrznego jest o trzy mniejsza od ich rzędu.

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  • INFLUENCE OF A VERTEX REMOVING ON THE CONNECTED DOMINATION NUMBER – APPLICATION TO AD-HOC WIRELESS NETWORKS

    Publikacja

    - 2015

    A minimum connected dominating set (MCDS) can be used as virtual backbone in ad-hoc wireless networks for efficient routing and broadcasting tasks. To find the MCDS is an NP- complete problem even in unit disk graphs. Many suboptimal algorithms are reported in the literature to find the MCDS using local information instead to use global network knowledge, achieving an important reduction in complexity. Since a wireless network...

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  • FPGA computation of magnitude of complex numbers using modified CORDIC algorithm

    In this work we present computation of the magnitude of complex numbers using a modified version of the CORDIC algorithm that uses only five iterations. The relationship between the computation error and the number of CORDIC iterations are presented for floating-point and integer arithmetics. The proposed modification of CORDIC for integer arithmetic relies upon the introduction of correction once basic computations are performed...

  • The Backbone Coloring Problem for Small Graphs

    In this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...

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  • On-line Ramsey Numbers of Paths and Cycles

    Publikacja

    Consider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the \emph{on-line Ramsey number} $\tilde{r}(G,H)$. In...

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  • Krzysztof Gierłowski dr inż.

    Krzysztof Gierłowski uzyskał tytuł doktora inżyniera telekomunikacji na Wydziale Elektroniki, Telekomunikacji i Informatyki w 2018 roku. Jest autorem lub współautorem ponad 80 publikacji naukowych oraz recenzentem wielu czasopism i konferencji. Brał udział w szeregu projektów badawczych dotyczących tematyki IT, wliczając w to: finansowany ze źródeł UE projekt Inżynieria Internetu Przyszłości, projekt infrastrukturalny PL-LAB2020,...

  • Lower bound on the weakly connected domination number of a tree

    Publikacja

    Praca dotyczy dolnego ograniczenia liczby dominowania słabo spójnego w drzewach (ograniczenie ze względu na ilość wierzchołków i ilość wierzchołków końcowych w drzewie).