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Analysis of the 4-Cycle Systems and Investigation of the D-Maximal and D-Avoiding Systems

Bagheri, Yousef | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49145 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahmoodian, Ebadollah
  7. Abstract:
  8. Decomposition of a graph into it’s subgraphs is an important problem in Graph Theory and Combinatorics. In this thesis we investigate some papers and their results about the problem of the decomposition of a complete graph into 4−cycles. In chapter 1 we express some parts of a paper written by Bryant, Darryn, Horsley, Daniel, and Pettersson. After giving some definitions and notations about cycle systems and their spectrums, we use methods of the paper to give a proof for a theorem on the existence of a decomposition of complete graphs into 4−cycles. In the next three chapters we explain results of a paper written by Bryant, Darryn, Grannell, Mike, Griggs, Terry, and Mačaj, Martin. chapter 2 is about the trades and configurations of the 4−cycle systems and we give a proof for the number of non-isomorphic trades of the volume 3 and foundation 7, and in chapter 3 and 4 we investigate D−avoiding 4−cycle systems and D−maximal 4−cycle systems, respectively. In chapter 5 we pay attention to a paper written by Dejter, Rivera-Vega and Rosa, and we analyze the decomposition of K9 into 4−cycles which is the smallest basic complete graph that can be decompose to 4−cycles. Finally, in chapter 6 we investigate the a paper written by Adams and Bryant about Diagonally switchable 4-cycle systems
  9. Keywords:
  10. Steiner Triple System (STS) ; Graph Decomposition ; 4-Cycle Systems ; Trade ; Nonisomorphic Decomposition

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