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Algebraic Topology Metheds on Graph Coloring

Pouria Omidi | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53932 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Jafari, Amir
  7. Abstract:
  8. The aim of this thesis is to introduce some algebraic topologies methods and apply them on fining the chromatic number of some famous graphs and also hypergraphs. In the first part, we will use a mixture of two well-known technics, Tucker lemma and Discrete Morse theory to find an upper bound for the chromatic number of s-stable Kneser for some specific vector s. to find the sharper upper bound, we will deviate our strategy and use another approach by finding an edge-labeling and apply some theorems in POSET algebraic topology. In this way, we also find a connection between Young diagrams and the numbers of spheres in the box complex related to Kneser graphs and hypergraph. Actually, we can find its number
  9. Keywords:
  10. Chromatic Number ; Simplicial Complex ; Kneser Hypergraph ; Kneser Graph ; Stable Graphs ; Borsuk–Ulam Theorem ; Graph Coloring

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