Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Θηλυκός Μ. Δημήτριος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Extremal Graph Theory: Basic Results
Translated title:
Extremal Graph Theory: Basic Results
Summary:
In this thesis, we take a general overview of extremal graph theory, investigating
common techniques and how they apply to some of the more celebrated results in
the field. The first chapter is an introduction to the subject and some preliminary
definitions and results. The second chapter concerns substructures in dense graphs
and focuses on important results such as Turán’s theorem, Szemerédi’s regularity
lemma and the Erdős-Stone-Simonovits theorem. The third chapter concerns substructures in sparse graphs and investigates conditions which force a graph to contain a certain minor or topological minor. The fourth and final chapter is an introduction to the extremal theory of r-uniform hypergraphs and consists of a presentation of results concerning the conditions which force them to contain a complete r-graph and a Hamiltonian cycle.
Main subject category:
Science
Keywords:
graph theory, extremal graph theory, Turán, Szemerédi
