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Nekonečné matroidy
Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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Circuits and matchings in graphs
Tesař, Karel ; Pangrác, Ondřej (advisor) ; Šámal, Robert (referee)
O grafu řekneme, že je k-linkovaný, pokud pro každých k dvojic jeho vrchol· existují navzájem disjunktní cesty, které dané dvojice spojují. Existuje vztah mezi k-linkovaností a vrcholovou souvislostí grafu. V této práci hledáme vztah mezi vrcholovou souvislostí grafu a vlastností, že každých k jeho disjunktních hran leží na společné kružnici. Tento problém se dá řešit pomocí k-linkovanosti. Naším cílem je dosáhnout lepších odhad· na souvislost, resp. jiných postačujících podmínek než těch, které jsou známe pro k-linkovanost. 1
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Výrazové prvky současné architektury
Kokolia Křížová, Iveta
In the recent years, the process of architectural design has been evolving in a number of different ways, as it has always been the case. The goal, however, remains the same - to design a quality architecture. New forms and architectural elements have also emerged with the advent of modern technologies. What are the defined facts that enter into design and reveal the boundary between high-quality architecture and mere „building“? What signs could define the current period?
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Souvislost a resilience grafů
Novotná, Jitka ; Pangrác, Ondřej (advisor) ; Šámal, Robert (referee)
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)
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Decompositions of graphs into connected subgraphs
Musílek, Jan ; Pangrác, Ondřej (advisor) ; Fiala, Jiří (referee)
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.
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Nekonečné matroidy
Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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Circuits and matchings in graphs
Tesař, Karel ; Pangrác, Ondřej (advisor) ; Šámal, Robert (referee)
O grafu řekneme, že je k-linkovaný, pokud pro každých k dvojic jeho vrchol· existují navzájem disjunktní cesty, které dané dvojice spojují. Existuje vztah mezi k-linkovaností a vrcholovou souvislostí grafu. V této práci hledáme vztah mezi vrcholovou souvislostí grafu a vlastností, že každých k jeho disjunktních hran leží na společné kružnici. Tento problém se dá řešit pomocí k-linkovanosti. Naším cílem je dosáhnout lepších odhad· na souvislost, resp. jiných postačujících podmínek než těch, které jsou známe pro k-linkovanost. 1
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Journey - Mountain to circumvention
Hůlová, Martina ; Kornatovský, Jiří (advisor) ; Hůla, Zdenek (referee)
This thesis presents my personal view of the art and the world around us. Primary issue is the understanding of life and art as a journey and an infinite search. Based on this perspective, the specific topics like art, forms and means of expression, symbolism, concept of a journey, time and work of different artists are being surveyed both generally and specifically. Through the survey of those topics, connections and coherences are being found. This thesis also consists of an analysis of my own art work (painting) and my didactic praxis together with a subject of didactics. The elements of contemplation penetrate the entire thesis.
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Customer sattisfaction and its connection with financial results of retail chains
Výletová, Zuzana ; Šálková, Daniela (advisor) ; Tomáš, Tomáš (referee)
This diploma thesis studies potential coherence between customer satisfaction and economic results of retail chains. The thesis consists of theoretical and practical parts. In the theoretical part important terms connected with satisfaction, customers, trade and retail are defined. In the practical part can be found questionnaire research results and revenues of each retail chain. Questionnaires which were focused on customer satisfaction are evaluated by pivot tables and the results are displayed in graphs. The thesis disposes of retail chains revenues from years 2012, 2013 and 2014. The main aim of this diploma thesis is to find out if there is a possible coherence between customer satisfaction and revenues of concrete retail chains. This possible coherence is investigated by correlative coefficient. Based on the results of this thesis suggestions for improvement of concrete retail chains are made.
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