Topological Graph Theory

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Najafian, Abolfazl | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54243 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
The primary goal of this thesis is to study the chromatic number of Kneser hypergraphs that made a connection between topology and combinatorics.We mention simplicial complexes, Fan’s and Tuckers lemma’s, nerve’s lemma,and topological Tverberg theorem as some tools for investigating the chromatic number of these graphs. Many of the concepts and propositions expressed in this paper, such as those mentioned above, are topological propositions about combinatorial objects, and vice versa. Using such connections, you can use the tools of each branch in another and use their combination
Keywords:
Simplicial Complex ; Kneser Hypergraph ; Tverberg’s Theorem ; Topological Graph Theory