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Petersen coloring and variants
Bílková, Hana ; Šámal, Robert (advisor) ; Dvořák, Zdeněk (referee)
The Petersen coloring of 3-regular graph G is equivalent to the normal coloring by five colors. The normal coloring is a good coloring of edges such that every edge and its four neighbours have together three or five different colors. Jaeger conjectures that every bridgeless 3-regular graph has a Petersen coloring. If the conjecture were true, it would imply other interesting statements about 3-regular graphs. In this text we investigate normal coloring by more than five colors. Jaeger theorem about nowhere-zero Z2 3 -flow implies that every bridgeless graph has normal coloring by seven colors. Independently on the Jaeger theorem, we prove the existence of normal coloring by nine colors for graphs with a bridge, a cut of size two or with a triangle. The idea of our proof comes from Andersen's proof of existence of strong coloring by ten colors for 3-regular graphs. Finally, we sketch the idea of the proof for other classes of 3-regular graphs. 1
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Synthesis of cycles using organocatalysis and catalysis with metal complexes
Hurný, David ; Veselý, Jan (advisor) ; Trnka, Tomáš (referee)
This thesis deals with an enantioselective synthesis of cyclic compounds by using a combination of organocatalysis and transition metal catalysis. The thesis deals mainly with usage of aminocatalyst for activation of aldehydes and copper catalyst for activation of terminal triple bond. The first part is focused on the preparation of starting compounds for cyclizations (α-oxoesters, α- substituted nitroalkanes and α-substituted aldehydes). The second part concerns carbocyclization itself and optimization of reaction conditions to achieve highly stereoselective reaction. Powered by TCPDF (www.tcpdf.org)
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Domestic violence as a cycle and process in empirical research
Vlasáková, Dana ; Buriánek, Jiří (advisor) ; Vinopal, Jiří (referee)
(in English): Dissertation deals with the problematics of domestic violence from the perspective of empirical research. First, it discusses the definition of domestic violence with all its types and forms. Then it introduces possible typology of domestic violence conducted based on the frequency, cruelty, purpose and consequences of violent incidents and it identifies the most serious type of domestic violence known as intimate terrorism. It is characterized by cyclically repeating phases of partner's violent attacks and gradation of frequency and intensity of these attacks. Violent behavior is in this case guided by the motivation to dominate, control and intimidate the other partner. Next, it brings overview of risk factors and main sociological theories trying to explain the initiation and progress of domestic violence, starting from the Social Learning Theory, through the Social Situational/Stress and Coping Theory, Resource Theory, Exchange Theory, Sociobiological Theory, all the way to the Feminist Theories applied in subsequent interpretation of the results of the data analysis. Before the data analysis itself the dissertation describes the sources of the data and it introduces main moments of the research of domestic violence both in the world and in our country. Then it identifies a group...
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Synthesis of cycles using organocatalysis and catalysis with metal complexes
Hurný, David ; Veselý, Jan (advisor) ; Trnka, Tomáš (referee)
This thesis deals with an enantioselective synthesis of cyclic compounds by using a combination of organocatalysis and transition metal catalysis. The thesis deals mainly with usage of aminocatalyst for activation of aldehydes and copper catalyst for activation of terminal triple bond. The first part is focused on the preparation of starting compounds for cyclizations (α-oxoesters, α- substituted nitroalkanes and α-substituted aldehydes). The second part concerns carbocyclization itself and optimization of reaction conditions to achieve highly stereoselective reaction. Powered by TCPDF (www.tcpdf.org)
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Variants of Petersen coloring for some graph classes
Bílková, Hana ; Šámal, Robert (advisor) ; Rollová, Edita (referee)
Normal coloring - an equivalent version of Petersen coloring - is a special proper 5-edge-coloring of cubic graphs. Every edge in a normally colored graph is normal, i.e. it uses together with its four neighbours either only three colors or all five colors. Jaeger conjectured that every bridgeless cubic graph has a normal coloring. This conjecture, if true, imply for example Cycle double cover conjecture. Here we solve a weakened version of Jaeger's problem. We are looking for a proper 5-edge-coloring such that at least a part of the edges is normal. We show a coloring of generalized prisms with two thirds of the edges normal and a coloring of graphs without short cycles with almost half of the edges normal. Then we propose a new approach to normal coloring - chains. We use chains to prove that there cannot be only one single mistake in an almost normally colored graph. We also prove some statements about cuts in a normally colored graph which also follow from nowhere-zero Petersen flow. Finally, we examine a four-cycle in a normally colored graph. 1
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Petersen coloring and variants
Bílková, Hana ; Šámal, Robert (advisor) ; Dvořák, Zdeněk (referee)
The Petersen coloring of 3-regular graph G is equivalent to the normal coloring by five colors. The normal coloring is a good coloring of edges such that every edge and its four neighbours have together three or five different colors. Jaeger conjectures that every bridgeless 3-regular graph has a Petersen coloring. If the conjecture were true, it would imply other interesting statements about 3-regular graphs. In this text we investigate normal coloring by more than five colors. Jaeger theorem about nowhere-zero Z2 3 -flow implies that every bridgeless graph has normal coloring by seven colors. Independently on the Jaeger theorem, we prove the existence of normal coloring by nine colors for graphs with a bridge, a cut of size two or with a triangle. The idea of our proof comes from Andersen's proof of existence of strong coloring by ten colors for 3-regular graphs. Finally, we sketch the idea of the proof for other classes of 3-regular graphs. 1
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