Alecu, Bogdan (2021) A parametric approach to hereditary classes. PhD thesis, University of Warwick.

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Abstract

The “minimal class approach" consists of studying downwards-closed properties of hereditary graph classes (such as boundedness of a certain parameter within the class) by identifying the minimal obstructions to those properties. In this thesis, we look at various hereditary classes through this lens. In practice, this often amounts to analysing the structure of those classes by characterising boundedness of certain graph parameters within them. However, there is more to it than this: while adopting the minimal class viewpoint, we encounter a variety of interesting notions and problems { some more loosely related to the approach than others. The thesis compiles the author's work in the ensuing research directions.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Graph theory, Representations of graphs, Ramsey numbers, Bipartite graphs
Official Date:	June 2021
Dates:	Date Event June 2021 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Lozin, Vadim, 1962-
Sponsors:	Engineering and Physical Sciences Research Council
Format of File:	pdf
Extent:	vii, 181 leaves : illustrations
Language:	eng

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