Original title: Definovatelne grafy
Translated title: Definable graphs
Authors: Grebík, Jan ; Chodounský, David (advisor) ; Kurka, Ondřej (referee) ; Zapletal, Jindřich (referee)
Document type: Doctoral theses
Year: 2020
Language: eng
Abstract: [eng] [cze]
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 Práce 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
Keywords: Borel reducibility; dichotomy; graphings; graphons; graphs; orbit equivalence relation; Polish group; Borelovska reducibilita; dichotomie; grafy; graphingy; graphony; orbitova equivalence; Polska grupa

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/123575

Permalink: http://www.nusl.cz/ntk/nusl-490786


The record appears in these collections:
Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Doctoral theses