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| Author(s): |
Lucas Silva Sinzato Real
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2024-03-07 |
| Examining board members: |
Leandro Fiorini Aurichi;
Christina Brech;
Miriam Garcia Manoel;
Daniel Vendruscolo
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| Advisor: | Leandro Fiorini Aurichi |
| Abstract | |
The study of infinite graphs consists in a singular area from graph theory. In general, its problems cannot be approached by counting principles or optimizing algorithms, typical tools from finite combinatorics. In fact, a sort of arguments that support proofs in infinite graph theory are inherited from other branches of mathematics, mainly those in which the notion of infinite itself is a matter of study. Regarding that, this work lies in the intersection between graph theory, set theory and topology, where some problems from first area will be analysed under a viewpoint of the others. With some special depth, we will study the unfriendly partition conjecture and its state of art, as well as the notion of ends in infinite graphs and their applications. Incidentally, besides revisiting the literature concerning these discussions, this dissertation contributes original results. (AU) | |
| FAPESP's process: | 21/13373-6 - A study of infinite graphs through the problem of describing Unfriendly Partitions |
| Grantee: | Lucas Silva Sinzato Real |
| Support Opportunities: | Scholarships in Brazil - Master |