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Turán and Ramsey numbers for 3-uniform hyperpaths
Eliza Jackowska-Boryc
Abstract
The main subject of this dissertation are Ramsey and Turán numbers for the 3-uniform loose path P of length 3. We began by introducing the basic terminology and our results related to Ramsey and Turán numbers. In chapter 1, we formulated the most crucial result - Theorem 2.2. It gives the exact value for Ramsey number R(P;r)=r+6, for a number of colors less than 8. One of the most important method in determining Ramsey numbers is an application of Turán numbers. In order to prove Theorem 2.2. we had to use Erdős-Ko-Rado Theorem and Theorem related to Turán number for a triangle. The most important Turán-type Theorem is 2.7, which determines Turán number for P, for all n. Moreover, in chapter 2, we stated Theorems 2.9 and 2.10, which were extensions of a standard approach of Turán number- Turán numbers of the second and the third order. Those Theorems appeared to be very useful in the proof of Theorem 2.2, which was introduced in chapter 3. In chapter 4, w focused on conditional Turán numbers and their applications in the proofs of Theorem 2.7. The last chapter 5 was devoted to the presentation of the proofs of remaining theorems.- Record ID
- UAM6db86f6837e34277b79e022763352e00
- Diploma type
- Doctor of Philosophy
- Author
- Eliza Jackowska-Boryc (SNŚ/WMiI/FoMaCS) Eliza Jackowska-Boryc
- Title in Polish
- Liczby Turána i Ramseya dla 3-jednolitych ścieżek
- Title in English
- Turán and Ramsey numbers for 3-uniform hyperpaths
- Language
- en English
- Certifying Unit
- Faculty of Mathematics and Computer Science (SNŚ/WMiI/FoMaCS)
- Discipline
- mathematics / (mathematics domain) / (physical sciences)
- Scientific discipline (2.0)
- Defense Date
- 16-11-2018
- Title date
- 16-11-2018
- Supervisor
- URL
- http://hdl.handle.net/10593/24111 opening in a new tab
- Keywords in English
- Turán number, Ramsey number, hypergraph, path
- Abstract in English
- The main subject of this dissertation are Ramsey and Turán numbers for the 3-uniform loose path P of length 3. We began by introducing the basic terminology and our results related to Ramsey and Turán numbers. In chapter 1, we formulated the most crucial result - Theorem 2.2. It gives the exact value for Ramsey number R(P;r)=r+6, for a number of colors less than 8. One of the most important method in determining Ramsey numbers is an application of Turán numbers. In order to prove Theorem 2.2. we had to use Erdős-Ko-Rado Theorem and Theorem related to Turán number for a triangle. The most important Turán-type Theorem is 2.7, which determines Turán number for P, for all n. Moreover, in chapter 2, we stated Theorems 2.9 and 2.10, which were extensions of a standard approach of Turán number- Turán numbers of the second and the third order. Those Theorems appeared to be very useful in the proof of Theorem 2.2, which was introduced in chapter 3. In chapter 4, w focused on conditional Turán numbers and their applications in the proofs of Theorem 2.7. The last chapter 5 was devoted to the presentation of the proofs of remaining theorems.
- Thesis file
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- File: 1
- Turán and Ramsey numbers for 3-uniform hyperpaths, File Eliza doktorat ver2.pdf / 3 MB
- Eliza doktorat ver2.pdf
- publication date: 02-01-2020
- Turán and Ramsey numbers for 3-uniform hyperpaths, File Eliza doktorat ver2.pdf / 3 MB
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- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/phd/UAM6db86f6837e34277b79e022763352e00/