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Search results for: COMPLETE BIPARTITE GRAPHS
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On domination multisubdivision number of unicyclic graphs
PublicationThe 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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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines
PublicationIn this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. Our research stems from the works of Bodlaender, Jansen, and Woeginger (1994) and Bodlaender and Jansen (1993). In particular, we pursue the...
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On-line ranking of split graphs
PublicationA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Graphs with isolation number equal to one third of the order
PublicationA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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On quantum cryptography with bipartite bound entangled states
PublicationOstatnio pokazano bezpośrednie zastosowanie splątania związanego w kryptografii kwantowej. W niniejszym artykule dokonano przeglądu niektórych najnowszych osiągnięć dotyczących tego zagadnienia. W szczególności przypomniano istotne pojęcia i definicje. Ponadto podano nową konstrukcję stanów o splątaniu związanym, posiadających bezpieczne korelacje, dostarczając w ten sposób niskowymiarowe (6x6) stany o splątaniu związanym z niezerowym...
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Rotationally invariant bipartite states and bound entanglement
PublicationW pracy rozważano stany kwantowe niezmiennicze na działanie grupy SO(3). Pokazano, że w przypadku, gdy pierwszy podukład ma parzysty wymiar większy lub równy cztery oraz drugi podukład ma wymiar dowolny, większy niż pierwszy to pośród takich stanów zawsze istnieje splątanie związane.
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Equitable colorings of some variation of corona products of cubic graphs
PublicationThe problem of determining the value of equitable chromatic number for multicoronas of cubic graphs is studied. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use almost optimal number of colors in the remaining cases.
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Parity vertex colouring of graphs
PublicationA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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The paired-domination and the upper paired-domination numbers of graphs
PublicationIn 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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On the size of identifying codes in triangle-free graphs
PublicationIn an undirected graph G, a subset C⊆V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let gammaID(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected...
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All graphs with paired-domination number two less than their order
PublicationLet G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...
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Domination-Related Parameters in Rooted Product Graphs
PublicationAbstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.
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Experimental certification of an informationally complete quantum measurement in a device-independent protocol
PublicationMinimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d2-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information.Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first...
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Secure Italian domination in graphs
PublicationAn Italian dominating function (IDF) on a graph G is a function f:V(G)→{0,1,2} such that for every vertex v with f(v)=0, the total weight of f assigned to the neighbours of v is at least two, i.e., ∑u∈NG(v)f(u)≥2. For any function f:V(G)→{0,1,2} and any pair of adjacent vertices with f(v)=0 and u with f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) whenever x∈V(G)∖{u,v}. A secure Italian dominating...
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublicationA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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Synchronous black hole search in directed graphs
PublicationThe paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one...
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On Symmetry of Uniform and Preferential Attachment Graphs
PublicationMotivated by the problem of graph structure compression under realistic source models, we study the symmetry behavior of preferential and uniform attachment graphs. These are two dynamic models of network growth in which new nodes attach to a constant number m of existing ones according to some attachment scheme. We prove symmetry results for m=1 and 2 , and we conjecture that for m≥3 , both models yield asymmetry with high...
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Equitable coloring of graphs. Recent theoretical results and new practical algorithms
PublicationIn this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
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Approximation algorithms for job scheduling with block-type conflict graphs
PublicationThe problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...
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Average distance is submultiplicative and subadditive with respect to the strong product of graphs
PublicationWe show that the average distance is submultiplicative and subadditive on the set of non-trivial connected graphs with respect to the strong product. We also give an application of the above-mentioned result.
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COVID-19 severity forecast based on machine learning and complete blood count data
PublicationProper triage of COVID-19 patients is a key factor in eective case management, especially with limited and insucient resources. In this paper, we propose a machine-aided diagnostic system to predict how badly a patient with COVID-19 will develop disease. The prognosis of this type is based on the parameters of commonly used complete blood count tests, which makes it possible to obtain data from a wide range of patients.We chose...
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COVID-19 severity forecast based on machine learning and complete blood count data
PublicationProper triage of COVID-19 patients is a key factor in eective case management, especially with limited and insucient resources. In this paper, we propose a machine-aided diagnostic system to predict how badly a patient with COVID-19 will develop disease. The prognosis of this type is based on the parameters of commonly used complete blood count tests, which makes it possible to obtain data from a wide range of patients.We chose...
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Free randomness amplification using bipartite chain correlations
PublicationA direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of...
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Direct measurement of nonlinear properties of bipartite quantum states
PublicationNieliniowe własności stanów kwantowych, takie jak entropia, splątania, określają ilość ważnych fizycznych źródeł i są często używane w informatyce kwantowej. Na ogół są one obliczane z pełnego opisu stanu kwantowego, pomimo tego, że zależą od niewielkiej ilości parametrów opisujących dany stan. Wyciągamy nielokalną i nieliniową wielkość, mianowicie entropię Renyi, z lokalnych pomiarów dwóch par fotonów splątanych polaryzacyjnie.
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Towards Increasing Density of Relations in Category Graphs
PublicationIn the chapter we propose methods for identifying new associations between Wikipedia categories. The first method is based on Bag-of-Words (BOW) representation of Wikipedia articles. Using similarity of the articles belonging to different categories allows to calculate the information about categories similarity. The second method is based on average scores given to categories while categorizing documents by our dedicated score-based...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines: Complexity and Algorithms
PublicationIn this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality:...
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Optimal backbone coloring of split graphs with matching backbones
PublicationFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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Distributed Evacuation in Graphs with Multiple Exits
PublicationWe consider the problem of efficient evacuation using multiple exits. We formulate this problem as a discrete problem on graphs where mobile agents located in distinct nodes of a given graph must quickly reach one of multiple possible exit nodes, while avoiding congestion and bottlenecks. Each node of the graph has the capacity of holding at most one agent at each time step. Thus, the agents must choose their movements strategy...
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Connection graphs
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Decontaminating Arbitrary Graphs by Mobile Agents: a Survey
PublicationA team of mobile agents starting from homebases need to visit and clean all nodes of the network. The goal is to find a strategy, which would be optimal in the sense of the number of needed entities, the number of moves performed by them or the completion time of the strategy. Currently, the field of distributed graph searching by a team of mobile agents is rapidly expanding and many new approaches and models are being presented...
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A complete example of experience konowledge structure on XML
PublicationPrzedstawiono kompletny przykład reprezentacji struktury wiedzy w języku XML. Omówiono cztery podstawowe składniki tej reprezentacji: dane, funkcje, ograniczenia i zasady.
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A computer system for the complete design of ship propellers
PublicationPraca zawiera opis metody obliczeniowej pozwalającej na zaprojektowanie okrętowej śruby napędowej dla również obliczeniowo wyznaczonego niejednorodnego pola prędkości za kadłubem statku o znanej geometrii i parametrach ruchu. Metoda pozwala na właściwe ujęcie efektu skali i konsekwencji obecności płetwy sterowej za projektowaną śrubą.
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The unrestricted global effort to complete the COOL trial
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Strong Monogamies of No-Signaling Violations for Bipartite Correlation Bell Inequalities
PublicationThe phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as...
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Machine-aided detection of SARS-CoV-2 from complete blood count
PublicationThe current gold standard for SARS-CoV-2 detection methods lacks the functionality to perform population screening. Complete blood count (CBC) tests are a cost-effective way to reach a wide range of people – e.g. according to the data of the Central Statistical Office of Poland from 2016, there are 3,000 blood diagnostic laboratories in Poland, and 46% of Polish people have at least one CBC test per year. In our work, we show...
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A Framework for Searching in Graphs in the Presence of Errors
PublicationWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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Recycling of raw materials, silicon wafers and complete solar cells from photovoltaic modules
PublicationPhotovoltaic modules (PVs) are an attractive way of generating electricity in reliable and maintenance-free systems with the use of solar energy. The average lifetime of photovoltaic modules is 25 to 30 years. To offset the negative impact of photovoltaic modules on the environment, it is necessary to introduce a long-term strategy that includes a complete lifecycle of all system components from the production phase through installation...
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Behavior Based Complete Coverage Task of Unknown Area by an Autonomous Mobile Robot SCORPION with Static Obstacles in Environment
PublicationIn the paper the behavior based control system of an autonomous mobile robot SCORPION is presented to execute the one of the most difficult navigation task, which is the complete coverage task of unknown area with static obstacles in the environment. The main principle assumed to design control system was that the robot should cover all area only once, if it possible, to optimize the length of path and energy consumption. All commercial...
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An Efficient Noisy Binary Search in Graphs via Median Approximation
PublicationConsider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target vertex in a graph by asking queries. Each query is conducted as follows: the strategy selects a vertex q and receives a reply v: if q is the target, then =, and if q is not the target, then v is a...
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Quantum strategies for rendezvous and domination tasks on graphs with mobile agents
PublicationThis paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...
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A collection of directed graphs for the minimum cycle mean weight computation
Open Research DataThis dataset contains definitions of the 16 directed graphs with weighted edges that were described in the following paper: Paweł Pilarczyk, A space-efficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 349--355, DOI: 10.22436/jmcs.020.04.08, URL: http://dx.doi.org/10.22436/jmcs.020.04.08 These...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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Analysis of the complete genome sequence of the lactococcal bacteriophage bIBB29
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The inflence of TiO2 structure on the complete decomposition of acetaldehyde gas
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Ipertrofan Revisited—The Proposal of the Complete Stereochemistry of Mepartricin A and B
PublicationBeing a methyl ester of partricin, the mepartricin complex is the active substance of a drug called Ipertrofan (Tricandil), which was proven to be useful in treatment of benign prostatic hyperplasia and chronic nonbacterial prostatitis/chronic pelvic pain syndrome. Nevertheless, no direct structural evidence on the stereochemistry of its components has been presented to date. In this contribution, we have conducted detailed, NMR-driven...
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Rank Coloring of Graphs.
PublicationRozdział jest poświęcony uporządkowanemu kolorowaniu grafów. Przedstawiono jego podstawowe własności oraz zastosowania praktyczne.
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Circular colorings of graphs.
PublicationRozdział poświęcony jest cyrkularnemu modelowi kolorowania krawędzi. Rozważana jest zarówno wersja wierzchołkowa i krawędziowa. Szczególny nacisk położono na złożoność obliczeniową i zastosowania dla omawianych modeli kolorowania.
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T-coloring of graphs.
PublicationNiniejszy rozdział omawia kontrastowe kolorowanie grafów. Podana została jego definicja i podstawowe własności, zastosowania oraz złożoność obliczeniowa problemów rozważanych w ramach tej dziedziny.
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Harmonions Coloring of Graphs.
PublicationProblem kolorowania grafów jest motywowany radionawigacją lotniczą, kompresją obrazów i in. W rozdziale podano podstawowe fakty dotyczące tego modelu kolorowania, a wsród nich dolne i górne oszacowania na liczbę harmoniczną i algorytm o złożoności 0 (mm3) dający bardzo dobre pokolorowania przybliżone.
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Classical coloring of graphs.
PublicationRozdział obejmuje klasyczne kolorowanie krawędzi i wierzołków w grafach prostych. Oprócz podstawowych definicji podane zostały najczęściej stosowane metody przybliżone oraz ich właściwości. Dodatkowo rozdział zawiera przegląd znanych benczmarków dla podanych metod w kontekście klasycznego modelu kolorowania.