
Circle packing and Möbius transformations
Porvichová, Janka ; Zeman, Peter (advisor) ; Kratochvíl, Jan (referee)
A graph can be represented by various geometric representations. In this work we focus on the circle packing representation. We state various concepts impor tant for proving results regarding this kind of representation. We introduce a known proof of existence of a circle packing for planar graphs and a proof of existence of a primaldual circle packing for 3connected graphs. Next, we focus on computational complexity of extending the representation for a given partial circle packing. We examine the proof of the theorem stating that deciding whet her such an extension exists is an NPhard problem. We introduce our theoretical algorithm for extension construction based on real RAM machine. 1


Computational complexity in graph theory
Melka, Jakub ; Kratochvíl, Jan (advisor) ; Fiala, Jiří (referee)
In the present work we study the problem of reconstructing a graph from its closed neighbourhood list. We will explore this problem, formulated by V. Sós, from the point of view of the fixed parameter complexity. We study the graph reconstruction problem in a more general setting, when the reconstructed graph is required to belong to some special graph class. In the present work we prove that this general problem lies in the complexity class FPT, when parametrized by the treewidth and maximum degree of the reconstructed graph, or by the number of certain special induced subgraphs if the reconstructed graph is 2degenerate. Also, we prove that the graph reconstruction problem lies in the complexity class XP when parametrized by the vertex cover number. Finally, we prove mutual independence of the results

 
 

Physiological mechanisms of abiotic stress tolerance in Sorghum bicolor
Kratochvíl, Jan ; Konrádová, Hana (advisor) ; Lhotáková, Zuzana (referee)
Current agriculture is facing a serious challenge of decreasing precipitation and irregular occurrence of drought periods including their unfavorable distribution during the vegetation season. This leads to growing interest in planting highly droughtresistant crops like sorghum. In comparison with other crops, sorghum excels in low water demand, though exhibits high susceptibility to low temperatures, which hampers its spread to new regions. Surprisingly, there is not enough information about the nature of sorghum's reaction to cold exposure. The aim of this diploma thesis was to describe reactions of young sorghum plants exposed to cold stress, low water availability and their combination and to verify the possibility of plant hardening through previous lowstress load. The special focus was paid to changes in carbohydrate metabolism, which plays generally very important role in plant defense reactions. The other analyzed physiological traits were leaf tissue osmotic potential, proline content and basic morphometric characteristics. Experimental design consisted of pot experiments conducted in growth chambers and the experiments performed under controlled conditions in vitro, using two sorghum genotypes "Ruzrok" and "01Z1800012". Both genotypes exhibited similar response to stress treatment....


Highdensity, Lowrise housing in Brno, Černá Pole
Kuba, Jonáš ; Kratochvíl, Jan (referee) ; Májek, Jan (advisor)
The aim of the thesis is to design a compact housing with appropriate public services in the current barracks area in Černá Pole which is 16.97 ha large. The project respects existing buildings as it continues with a block structure of urban rental houses. The result is the area unification and creating a new local centre. The project strives for a functional urban development as it emphasizes the concept functionality, clarity and purity.


Highdensity, Lowrise housing in Brno, Černá Pole
Janík, Tobiáš ; Kratochvíl, Jan (referee) ; Májek, Jan (advisor)
Subject of my diploma thesis is to design new residential neighborhood on sight currently occupied by Barracks in Brno, Černá Pole. It is little used in the moment and forms spacial barrier in city organism and is slowly detracting. New proposal integrates area into surrounding development and is trying to maximally utilize its positive aspects. On site is not proposed just quiet residential neighborhood, but also city hall, shops, college dorm, primary school and kindergarten, creating a balanced unit communicating with the surrounding area.


Highdensity, Lowrise housing in Brno, Černá Pole
Fajkusová, Kateřina ; Kratochvíl, Jan (referee) ; Májek, Jan (advisor)
This diploma thesis deals with the urban study on the revitalization of the barracks in Brno, the Black Fields. In the defined area a new residential complex is designed to integrate the area into the surrounding area. The proposal also envisages the creation of development areas for Mendel University, where within these areas will be created a sports hall, accommodation facilities for students library and a representative building. An interesting element is the creation of a public space shielded from traffic.

 

Computational Complexity in Graph Theory
Jelínková, Eva ; Kratochvíl, Jan (advisor) ; Manlove, David (referee) ; Fiala, Jiří (referee)
Title: Computational Complexity in Graph Theory Author: Eva Jelínková Department: Department of Applied Mathematics Supervisor: Prof. RNDr. Jan Kratochvíl, CSc., Department of Applied Mathematics Abstract: We address problems from graph theory, especially from the computational complexity point of view. In the first part of the thesis we address the computational complexity of problems related to Seidel's switch ing of graphs. We prove that the problem to decide if a given graph can be switched to contain at most a given number of edges is NPcomplete, even for graphs with bounded density. We thus partially answer a question of Matoušek and Wagner [Discrete Comput. Geom. 52, no. 1, 2014]. We also describe infinitely many graphs H such that it is NPcomplete to decide if a given graph is switchingequivalent to a graph that does not contain H as an induced subgraph. We thus close an open problem of Kratochvíl, Nešetřil and Zýka [Annals of Discrete Math. 51, 1992]. In the second part of the thesis we address the topic of matchings under preferences. We focus on the housing market problem, in particular, on the model with duplicate houses. We present a 2approximation algorithm for the maximum number of satisfied agents when the preference lists of agents are trichotomic. On the other hand, we...
