Erdős-Rényijev model slučajnih grafova

master's thesis

• Author: Monika Bajcer
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-11-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučava se tema slučajnih grafova, koja se može predstaviti kao spoj teorije vjerojatnosti i teorije grafova. Definira se slučajni graf kao vjerojatnosni prostor nad skupom svih grafova sa fiksiranim skupom vrhova. Također se proučavaju neka svojstva slučajnih grafova kao što je najveća klika u grafu, monotona svojstva i njihove prijelazne funkcije, zakoni nula-jedan i Erdős-Rényijeva promjena faze.

Abstract (english)

This thesis contributes to the topic of random graphs, which combines probability theory and graph theory. It gives the definition of random graph as a probability space over the set of graphs on a fixed vertex set. Also, it discusses some random graphs properties and phenomena like clique number, monotone properties and their threshold functions, zeroone laws and the Erdős-Rényi phase transition.

• Keywords: slučajni graf; Erdős-Rényijev model; Erdős-Rényijeva promjena faze
• Keywords (english): random graphs; Erdős-Rényi model; Erdős-Rényi phase transition
• Language: croatian
• URN:NBN: urn:nbn:hr:217:391649
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-01-30 12:21:48