CEU Electronic Theses and Dissertations, 2021
| Author | Salia, Nika |
|---|---|
| Title | Extremal problems for paths and cycles |
| Summary | A classical result of Erd\H{o}s and Gallai determines the maximum number of edges in a simple $n$ vertex graph without a path of given length as a subgraph, i.e. they determined Tur\'an number of paths. They also determined Tur\'an number of a class of long cycles. In this dissertation, we extend those results for Hypergraphs. We follow one of the most general definitions of paths and cycles in hypergraphs. A Berge-path of length $k$ in a hypergraph $\h$ is a sequence $v_1,e_1,v_2,e_ 2,\dots,v_{k},e _k,v_{k+1}$ of distinct vertices and hyperedges with $v_{i+1}\in e_i,e_{i+1}$ for all~$i\in[k]$. Berge-cycles are defined similarly. We study several generalizations of Erd\H{o}s-Gallai theorem for hypergraphs forbidding Berge families of paths and cycles and some related problems. |
| Supervisor | Győri, Ervin |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2021/salia_nika.pdf |
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