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Fuzzy graphs theory
Ducký, Patrik ; Zbořil, František (referee) ; Hliněná, Dana (advisor)
This bachelor thesis deals with the problems of fuzzy sets, fuzzy relations and their application in fuzzy graph theory. In the introduction, the basic problem of fuzzy sets is introduced. The next part of the thesis is devoted to the properties of fuzzy relations and their relation to fuzzy graphs. The main part of the thesis consists of classical coloring, fractional coloring of graphs and their fuzzification. Finally, an application is presented that can instruct the user on fractional coloring of fuzzy graphs, and at the same time can color the input fuzzy graph. The goal of this thesis and the application is to contribute to the awareness of this issue and its possible applications in computer science.
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Analýza genů podmiňujících zbarvení velkého münsterlandského ohaře
FRYŠOVÁ, Adéla
The target of this thesis was to obtain a sufficient number of DNA samples from individuals Breed Large Münsterländer and they perform genotyping newly described mutation c.555> G in exon 2 of the gene TYRP1. In the case of this mutation in the breed we studied, another aim of the work was to propose breeding measures that would limit the spread of this undesirable mutation. At the beginning of the literary overview, the breed of the great Münsterlander, his history, the breed, the standard with an emphasis on the permitted coloring and the current breeding of a large Mässlandlander in the Czech Republic. The thesis describes the individual genetic foundations of coloring and explains the principles of the methods used in their own work. In its own work genotyping was performed on the mutation in exon 2 of the TYRP1 gene by polymerase chain reaction and sequencing methods. This mutation was not demonstrated in either of the 113 tested individuals of the Greater Münsterlander. It was also used of the available commercial tests previously described mutations in the gene TYRP1 on which were worked out plans for auxiliary mating as an aid to farmers to avoid the herd to increase the number of recessive homozygotes undesirable brown coat color or heterozygotes, who carry a mutated allele.
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3-Coloring Graphs on Torus
Pekárek, Jakub ; Dvořák, Zdeněk (advisor) ; Šámal, Robert (referee)
The theory of Dvořák et al. shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the natural reduction in such embedded graphs-identification of opposite vertices in 4-faces. We give a computer-assisted argument showing that there are exactly four 4-critical triangle-free irreducible toroidal graphs in which this reduction cannot be applied without creating a triangle. Using this result we demonstrate several properties that are necessary for every triangle-free graph embedded in the torus to be 4-critical. Most importantly we demonstrate that every such graph has at most four 5-faces, or a 6-face and two 5-faces, or a 7-face and a 5-face, in addition to at least seven 4-faces.
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Barevnost grafů na plochách
Tůma, Vojtěch ; Dvořák, Zdeněk (advisor) ; Fiala, Jiří (referee)
In this thesis we deal with extending a 4-coloring of a cycle into the rest of the graph. We prove that for plane 3-colorable graphs such that every face except the outer face O is a triangle and O has length 4 or 5, the question of extendability of a precoloring of O reduces to extendability into 3 small basic graphs. We also classify the situation when there is an inner face of size 5 in the graph in similar terms. 1
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