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Connected Factor and 3-Vertex Factors on Graphs

Hasanvand, Morteza | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46581 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Akbari, Saieed
  7. Abstract:
  8. Let G be a graph. A P3-factor of graph G is a subgraph of G such that each component is isomorphic to P3. In 1985 Akiyama and Kano conjectured that every 3-connected 3-regular graph of order divisible by 3 has a P3-factor. In this thesis we conjecture that every 3-connected 4-regular graph of order divisible by 3 has a P3-factor and also show that this conjecture concludes the previous one. Moreover, we investigate connected factors and some 3-vertex induced factors in graphs and show that every r-regular graph of order n (3 j n) has a P3-induced factor, if r _> 8n/ 9-1
  9. Keywords:
  10. Regular Graph ; Bipartite Graph ; Connected Factors ; Induced Factor ; Three Vertex Factors

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