CEU Electronic Theses and Dissertations, 2013
| Author | Szécsi, Vajk |
|---|---|
| Title | Problems From Extremal Combinatorics |
| Summary | The thesis consists of multiple problems from the field of extremal combinatorics. Chapter 1&2: Introduction and notations Chapter 3:We determine the minimal length of the longest trail in a fixed edge-density graph. This result is similar to the Erdos-Gallai theorem describing the maximal size of a graph not containing a path of length l. Chapter 4: We determine the extremal behaviour of 3-uniform k-fan-free hypergraphs. Chapter 5: The concept of almost intersecting set systems is introduced and multiple possible definitions (=l, <=l,uniform, non-uniform) are examined. Chapter 6: the concept of cross-Sperner pairs of families is introduced and analysed. Chapter 7: Further almost-properties are introduced and analysed ('almost Sperner', 'almost intersecting Sperner' and 'almost unrelated' families) |
| Supervisor | Gyula O. H. Katona |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2013/szecsi_vajk.pdf |
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