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Substructure Densities in Extremal Combinatorics

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posted on 2021-06-19, 00:31 authored by TIMOTHY FONG NAM CHAN
One of the primary goals of combinatorial mathematics is to understand how an object's properties are influenced by the presence or multiplicity of a given substructure. Over time, it has become popular to highlight the asymptotic behaviour of objects by expressing results in terms of the density of substructures. In this thesis, we investigate three topics concerning combinatorial density: We study the interplay between the densities of cycles of length 3 and 4 in large tournaments, we characterise quasirandomness in permutations, and we solve two open problems about the inducibility of trees.


Campus location


Principal supervisor

David Wood

Additional supervisor 1

Daniel Kráľ

Year of Award


Department, School or Centre


Additional Institution or Organisation

University of Warwick


Doctor of Philosophy (Joint award with the University of Warwick)

Degree Type



Faculty of Science