Definable graphs
Definovatelne grafy
dissertation thesis (DEFENDED)
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Permanent link
http://hdl.handle.net/20.500.11956/123575Identifiers
Study Information System: 177569
CU Caralogue: 990023912890106986
Collections
- Kvalifikační práce [11368]
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Algebra, number theory, and mathematical logic
Department (external)
Information is unavailable
Date of defense
5. 5. 2020
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Pass
Keywords (Czech)
grafy, graphony, graphingy, dichotomie, Borelovska reducibilita, orbitova equivalence, Polska grupaKeywords (English)
graphs, graphons, graphings, dichotomy, Borel reducibility, orbit equivalence relation, Polish groupPráce se zabýva otázkami teorie grafu v kontextu deskriptivní teorie množin. Hlavní objekty studia jsou graphony, graphingy a variace na graf G0. Představíme přistup ke kompaktnosti prostoru graphonu pomocí slabě* topologie a pojem frakcionalního isomor- fismu graphonu. Použijeme variantu G0-dichotomie v kontextu klasifikačního problému. Dokážeme měritelnou verzi Vizingovi věty pro grafingy. 1
In this thesis we consider various questions and problems about graphs that appear in the framework of descriptive set theory. The main object of study are graphons, graphings and variations of the graph G0. We establish an approach to the compactness of the graphon space via the weak* topology and introduce the notion of a fractional isomorphism for graphons. We use a variant of the G0-dichotomy in the context of the classification problem. Finally, we show a measurable version of the Vizing's theorem for graphings. 1