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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Steiner coloring of cubic graphs
 Tlustá, Stanislava ; Fiala, Jiří (advisor) ; Šámal, Robert (referee)
This thesis is dedicated to the coloring of cubic graphs. It summarizes the knowledge we have about so called Steiner coloring, which is an edge-coloring such that the colors incident with one vertex form a triple of some partial Steiner system. The main objects of interest are the projective and affine systems. Afterwards the sufficient condition for universality of the system is stated and it is observed, that all other transitive Steiner triple systems satisfy it. This thesis also contains methods of construction of the coloring for the Fano plane, for the affine system Z3 3 and for the universal system created as a product of the Fano plane and the trivial system (F7 S⊠ 3). Finally an algorithm usable for the rest of the systems and graphs with bounded treewidth is presented.
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Maximal Orders
 Tlustá, Stanislava ; Příhoda, Pavel (advisor) ; Růžička, Pavel (referee)
Maximal Orders Stanislava Tlustá Abstract This thesis summarizes basic properties of lattices and orders over Dedekind domain in separable algebras. The concepts of reduced norm and reduced trace are introduced and applied to few examples of rational algebras. By that the maximal orders are found. The properties of maximal orders are stated and used to explore new types of ideals: normal ideals and Λ-ideals. At the end of this thesis the isomorphisms of lattices are examined and the Jordan-Zassenhaus theorem is proved. 1
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1 Tlustá, Sabina
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