Lopes Martins, Taísa (2018) Theory of combinatorial limits and extremal combinatorics. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Combinatorial analysis, Combinatorial group theory, Extremal problems (Mathematics), Graph theory
Official Date:	September 2018
Dates:	Date Event September 2018 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Králʼ, Daniel
Sponsors:	Ciência sem fronteiras ; European Research Council
Extent:	vi, 86 leaves
Language:	eng

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