Tutte Conjecture on Nowhere-zero Flow

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Moghaddam Zadeh, Mohammad Javad | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50697 (01)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
In this thesis, the notion of nowhere-zero flow on graphs in defined with values is an Abelian group. It is shown that the existence of nowhere-zero flow with values in H depends on only the cardinal of H. Also the existence of nowhere-zero flowwith values on Zk is equivalent to the existence of the nowhere-zero flow with values in the set 1,2,...,k-1 on group Z.It is a easily seen that the nowhere zero flow on the graph with bridge doesn’t exist. Also has been proved any graph with no bridge has nowhere-zero 6 flow.Concidentally, the existence of nowhere-zero 5 flow for graphs with no bridge isstill an open problem.In 3-flow case, recently it is shown that any 8-edge connected graph has nowherezero 3-flow. Finally the proof of this issue is presented. After that, the similar proposition has been proved for 6-edge conected graphs
Keywords:
Graph Theory ; Nowhere Zero Flow ; Tutte's Conjecture