Networks, model theory and combinatorics
| Thesis title in Czech: | Sítě, teorie modelů a kombinatorika |
|---|---|
| Thesis title in English: | Networks, model theory and combinatorics |
| Key words: | sítě|teorie modelů|grafové modely|limity struktur|v |
| English key words: | networks|model theory|graph models|structural limits |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Ing. et Ing. David Hartman, Ph.D. et Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 19.09.2023 |
| Date of assignment: | 19.09.2023 |
| Confirmed by Study dept. on: | 02.10.2023 |
| Advisors: | prof. RNDr. Jaroslav Nešetřil, DrSc. |
| Guidelines |
| The field of complex networks brought many new challenges to mathematics and particularly to combinatorics and graph theory. It also led to many problems of multidimensional nature involving probability, topology, dynamics and more recently model theory. Particularly classification problems, relate to some fundamental problems about graphs classes and networks and it is possible to say that this changes the whole perspective of this subject. The topic of this thesis is to further pursue this interplay and apply it to new problems particularly in the area of sparse networks and limit behavior and procedures for structures. |
| References |
| Lovász, L. (2012). Large Networks and Graph Limits. American Mathematical Society.
Nešetřil, J. & de Mendez, P. O. (2012). Sparsity: graphs, structures, and algorithms (Vol. 28). Springer Science & Business Media. Nešetřil, J. & de Mendez, P. O. (2020) A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth. Memoirs of The American Mathematical Society, 263(1272). Hodges, W. & Wilfrid, H. (1993). Model theory. Cambridge university press. |