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Title: Theory of combinatorial limits and extremal combinatorics
Author: Lopes Martins, Taísa
ISNI:       0000 0004 7657 932X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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In the past years, techniques from different areas of mathematics have been successfully applied in extremal combinatorics problems. Examples include applications of number theory, geometry and group theory in Ramsey theory and analytical methods to different problems in extremal combinatorics. By providing an analytic point of view of many discrete problems, the theory of combinatorial limits led to substantial results in many areas of mathematics and computer science, in particular in extremal combinatorics. In this thesis, we explore the connection between combinatorial limits and extremal combinatorics. In particular, we prove that extremal graph theory problemsmay have unique optimal solutions with arbitrarily complex structure, study a property closely related to Sidorenko's conjecture, one of the most important open problems in extremal combinatorics, and prove a 30-year old conjecture of Gyori and Tuza regarding decomposing the edges of a graph into triangles and edges.
Supervisor: Not available Sponsor: Ciência sem fronteiras ; European Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics