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Zugl.: Tübingen, Univ., Diss., 2003.

The thesis consists of a collection of my contributions to universal algebra. Motivated by the Constraint Satisfaction Problem (CSP), we study the algebras of polymorphisms of relational structures. We begin by showing by an algebraic argument (and a bit of calculus) that random relational structures' CSP is almost always NP-complete. We then study digraphs with a Maltsev polymorphism, and conclude that such digraphs must also have a majority polymorphism. Next, we show how to use absorption tech- niques to prove that congruence modular reflexive digraphs must have an NU operation. We close our work by giving an algebraic proof of a result (first obtained by graph theorists) that 3-conservative relational structures with only unary and binary relations either define NP-complete CSP, or CSP for them can be solved by the local consistency algorithm. 1

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In 2003 at Eurocomb conference J. Barát and C. Thomassen presented definition and basic results in edge partitioning of graphs. Edge partitioning is basically possibility to cover edges of the graph using connected subgraphs of prescribed size. Graph has edge partitioning property if and only if it can be covered for all prescribed subgraphs sizes. Our work is focused on edge partitioning, in which there are less results known, compared to vertex partitioning. We proof, that edge partitioning is implied by existence of open dominating trail and therefore with edge 4-connectivity. We also define limited version of edge partitioning, spectrum of partitioning and we proof some claims that are true for all graphs. We also explore limited partitioning on some specific classes of graphs.

A graph is k-resilient if it is possible to construct local routing tables for each vertex such that we can reach a specified destination vertex from anywhere in the graph. There is a conjecture that k-resilience is equivalent to (k+1)-connectivity. We prove this for 3-edge-connected graphs and 4-edge-connected planar triangulations. In the proof we use independent directed spanning trees. Two spanning trees are independent if they share no common edge with the same direction. For k=3,4 we show that a graph has k independent spanning trees if and only if it is k-edge-connected. We search for the spanning trees constructively through reductions of parts of the graph. Some of these reductions can also be used in a general k- connected case. Powered by TCPDF (www.tcpdf.org)

Manufactural activity is the basis of every sound economy. The risk for today's industrial establishments in our let us say european conditions is to hold competitiveness in the terms of global economy. This diploma thesis is focusing on solving problems of manufacturing scheduling with the view of theory and practice. It is impeach of real-life production. Scheduling belongs to hard combinatorial problems and therefore are usually solved by various heuristic or metaheuristic methods. For application of mentioned metaheuristic methods is important to use suitable choice of representative data.

This diploma thesis deals with various types of relations observable in social networks. First part contains survey of existing papers focused on social media data analysis and visualisations. This survey is followed by research of existing visualisation applications. The contribution of this thesis is a new look at relations on social networks, from the side of relationship between users who write posts on any given topic. To visualize these relations was chosen network graph. On the basis of established criteria existing instruments were evaluated and since any of them did not meet all requirements, I created new application for visualising relations. Thesis also includes a description of selection the appropriate libraries for its implementation, explanation of user interface and a summary of configuration options and customization. The end of the work contains analysis and visualisations made with newly-created tool.

In large measure the literary reputation of Aleksei Nikolaevich Tolstoi (1883-1945) rests on the historical novel Peter the First. Before the novel and during its writing, he also wrote stories and plays set in the past. However, literature written int the Soviet Union very often needs to be considered against the background of current events, and historical fiction especially cannot be regarded apart from state ideology or the fluctuations in the political climate. Between 1917 and 1945, Soviet interpretation of the Russian past changed from contentious class-consciousness and dialectical rejection, to a determined rehabilitation of select personalities whose life and accomplishments were supposed to inculcate Soviet patriotism. With his heightened sense of history, Tolstoi often sought, to rationalize contemporary conditions through representations of analogous periods in Russian history, and in this manner some of the works which are discussed in this study may be viewed as reflections of current events. On the other hand, altered political perspectives-of the Russian past required him to make radical modifications in works written a few years earlier, and to make some distortions of history in works he was about to write. But in addition to historical, cultural and political considerations, the discussion of Tolstoi's separate works will demand as well that some attention be paid to the writer's use of the Russian language as an instrument for creating a sense of the past. To facilitate the discussion of Tolstoi's historical fiction in this study, the works are grouped by genre and then arranged in chronological order. Chapter I, however, offers a biographical sketch of A. N. Tolstoi. This is important for the thesis because the writer's views and attitudes provide a key for a better understanding of the extra-literary influences which affected his work. In the second chapter, short stories are discussed, beginning with the anecdotes from 1909, in which there is little history save for the description of costumes and manners. But stories written during and immediately after the Russian revolution reflect Tolstoi's initial hostility to the Bolsheviks, then his apparent loss of interest in the political antagonisms between the White émigré's and the Reds, and finally his gradual acceptance of the Soviet regime. After his return to Soviet Russia, the stories assume an almost belligerent, Marxist tone. Tolstoi's magnum opus is discussed in the third chapter. Peter the First is presented in context of the historical novel in general, the contemporary Soviet historical novel, and finally in 'context-of contemporary criticism. A glimpse into the Petrine theme in Russian literature is also offered as a further contrast to Tolstovi's novel. Historical plays are reviewed in the fourth chapter, offering the best illustration of that political fluctuation that so blatantly forced the writer to change his work and to alter history as well. Chapter V concludes the study with a general and chronological summation of the works discussed; it demonstrated that in spite of the various extra-literary influences, Aleksei Tolstoi remains a major and talented figure among twentieth-century Russian writers. / Arts, Faculty of / Central Eastern Northern European Studies, Department of / Graduate

This thesis describes and analyzes the postal transportation network of Central Bohemian Region, shows an applications of operational management in transport and by Clarke - Wright algorithm with limited capacity of the vehicles and limited time of ride solves the design of new routes to reduce mileage while operating the branch network of the territory.