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Wyniki wyszukiwania dla: independence number
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On the independence number of some strong products of cycle-powers
PublikacjaIn the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers alpha((C^2_10)^⊠3) = 30 and alpha((C^4 _14)^⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish...
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Common Independence in Graphs
PublikacjaAbstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...
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Bounds on isolated scattering number
PublikacjaThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Bounds on isolated scattering number
PublikacjaThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Independence in uniform linear triangle-free hypergraphs
PublikacjaThe independence number a(H) of a hypergraph H is the maximum cardinality of a set of vertices of H that does not contain an edge of H. Generalizing Shearer’s classical lower bound on the independence number of triangle-free graphs Shearer (1991), and considerably improving recent results of Li and Zang (2006) and Chishti et al. (2014), we show a new lower bound for a(H) for an r-uniform linear triangle-free hypergraph H with r>=2.
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The Potential of Greed for Independence
PublikacjaThe well-known lower bound on the independence number of a graph due to Caro and Wei can be established as a performance guarantee of two natural and simple greedy algorithms or of a simple randomized algorithm. We study possible generalizations and improvements of these approaches using vertex weights and discuss conditions on so-called potential functions p(G) : V(G) -> N_0 defined on the vertex set of a graph G for which suitably...
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New potential functions for greedy independence and coloring
PublikacjaA 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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Graphs hard-to-process for greedy algorithm MIN
PublikacjaWe compare results of selected algorithms that approximate the independence number in terms of the quality of constructed solutions. Furthermore, we establish smallest hard- to-process graphs for the greedy algorithm MIN.
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Product Graph Invariants with Applications in the Theory of Information
PublikacjaThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Parity vertex colouring of graphs
PublikacjaA 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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Towards Emotion Acquisition in IT Usability Evaluation Context
PublikacjaThe paper concerns extension of IT usability studies with automatic analysis of the emotional state of a user. Affect recognition methods and emotion representation models are reviewed and evaluated for applicability in usability testing procedures. Accuracy of emotion recognition, susceptibility to disturbances, independence on human will and interference with usability testing procedures are...
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Female entrepreneurship in Kazakhstan
PublikacjaWomen constitute the majority of the Kazakh population and, even though they live almost 10 years longer than men on average, they are far less economically active. Less than half of the female population take up employment. Women’s wages are often as much as 30% lower than men’s. The subjective reasons for undertaking economic activity as mentioned by women included: independence from the husband, low earnings of the husband and...
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Organizacja systemu opieki nad seniorami wyzwaniem dla samorządów lokalnych
PublikacjaA significant part of the activities undertaken so far under the senior policy, also at the local level, have been focused on seniors’ social (physical and educational) activation. The growing number of the oldest seniors, with limited independence, living alone in single‑person households, away from their families, will force the policy priorities to be reoriented in such a way as to develop efforts to provide different types...
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Measurement of sub-nanometer molecular layers with ISFET without a reference electrode dependency
PublikacjaA new method of detection and measurement with sub-nanometer resolution of layers adsorbed or bonded to the ISFET's gate dielectric was presented. The sensitivity of this method is high enough to detect even partial mono-layer covering. The transconductance measurement of the ISFET provides independence of the output signal from pH changes and the driving electrode electrochemical potential instabilities. The stable reference electrode...
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NOMINATION DOSSIER, The Modernist Centre of Gdynia, parts 4 - 7
PublikacjaThe city of Gdynia is commonly known in Poland as a symbol of the country’s independence and evidence of the foresight of planners and politicians. It is the outcome of the efforts and aspirations of generations of people from all kinds of backgrounds who made Gdynia their home. Document prepared by researchers from Gdansk University of Technology and other experts is the important part of the Nomination Dossier prepared for international...
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Subadditivity of the minimum output entropy and superactivation of the classical capacity of quantum multiple access channels
PublikacjaWe study subadditivity of the minimum output entropy (Hmin) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for Hmin known in classical information theory. Our result is based on a fundamental property of MACs, i.e., independence of each sender. The channels used in the example can be constructed explicitly. On the basis of subadditivity of Hmin we also provide an example...
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Automatic evaluation of information credibility in Semantic Web and Knowledge Grid
PublikacjaThis article presents a novel algorithm for automatic estimation of information credibility. It concerns information collected in Knowledge Grid and Semantic Web. Possibilities to evaluate the credibility of information in such structures are much greater than those available for WWW sites which use natural language. The rating system presented in this paper estimates credibility automatically on the basis of the following metrics:...
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Preface of guest editors
PublikacjaA special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 12th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 16-21 September 2007 in Karpacz, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, 2003 and 2005 in Karpacz. About 70 participants formed the audience of six invited lectures and 68...
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Political relations between Poland and the Republic of Azerbaijan
PublikacjaPoland was one of the first countries to recognize the independence of the Republic of Azerbaijan. However, the political co-operation between the two countries was established only at the end of the last decade of the 20th century, during the presidency of Aleksander Kwaśniewski. The next Polish president – Lech Kaczyński – intending to diversify the energy sources, maintained political relations between Poland and the Republic...
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Experimental test of nonclassicality with arbitrarily low detection efficiency
PublikacjaWe theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking an extra assumption of independence of the devices. Our test and its implementation is set in a prepare-and-measure scenario with an upper limit on the classical communication capacity of the channel through which the systems are communicated. The essence for our...