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Vertex Coloring and Edge Coloring of Graphs

Fimi, Khadijeh | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56091 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Akbari, Saeed
  7. Abstract:
  8. In this thesis, we study some bounds for the vertex chromatic num- ber and edge chromatic number of a graph. One of the most fa- mous theorems on graph colorings is Brooks’ Theorem, which asserts that every connected graph with maximum degree ∆(G) is ∆(G)- colorable unless G is an odd cycle or a complete graph. The following result has been proved: If every vertex of a graph G lies on at most k odd cycles for some nonnegative integer k, then χ(G) 1+√8k+9 . We recall from Vizing’s Theorem that the edge chromatic number of any graph must be equal either to ∆(G) or ∆(G) + 1. In this thesis, families of graphs that are Class 1 or Class 2 will be introduced.
  9. Keywords:
  10. Vertex Coloring ; Graph Edge Coloring ; Edge Chromatic Number ; Vertex Chromatic Number ; Proper Edge Coloring ; Graph Coloring

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