Path and Cycle Factors in 3-Regular Graphs

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Haghparast, Nastaran | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45029 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
Given a graph G and a set F of connected graphs, an F-packing of G is a subgraph of G whose components are isomorphic to one member of F. In addition, if H is a subgraph of G, then an H-packing is defined similarly. The maximum F-packing is an F-packing such that it has the maximum number of vertices. If the F-packing F is a spanning subgraph of G, then F is called an F-factor. If each member of F is a path of order at least two (cycle), then an F-factor is called a path (cycle) factor. In this thesis, the focus was on the path factor and cycle factor in 3-regular graphs and these factors were investigated in 2-connected graphs, 3-connected graphs and bipartite graphs. Moreovere special attention was paid to the P3-factor in graphs and different bounds for the minimum number of vertices of maximum P3-packing in graph were presented
Keywords:
Cycle Factor ; Path Factor ; 3-Regular Graph ; Bipartite Graph ; P3-Factor