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Path Factors in Graphs

Rabinia Haratbar, Sanaz | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45173 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Akbari, Saeed
  7. Abstract:
  8. Let G be a graph. A path factor of a graph G is a family of distinct paths with at least two vertices which forms a partition for the vertices of G. For a family of non-isomorphic graphs, F; an F-packing of G is a subgraph of G such that each of its component is isomorphic to a member of F. An F-packing P of G is called an F-factor if the set of vertices in graph G and P are the same. The F-packing problem is the problem of finding an F-packing having the maximum number of vertices in G. In graph theory packing of the vertices of paths, cycles and stars are interesting subjects . This thesis is devoted to determine the conditions under which graph G has a {Pk}-factor, where by Pk we mean a path with k vertices. In this context, the existence of path factors in bipartite, r-regular, claw free and Line graphs are investigated. And more generally, some work is done on packing of vertices in a graph with distinct Pk. At the end we try to investigate packing of these families and propose some conjectures about them
  9. Keywords:
  10. F-Factor ; Path Factor ; Bipartite Graph ; F-Packing ; Linear Graph