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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... 

Let G be a graph and F : V (G) ...! 2N be a function. The graph G is said to be F-avoiding if there exists an orientation O of G such that d+ O(v) =2 F(v) for every v 2 V (G), where d+O(v) denotes the out-degree of v in the directed graph G with respect to O. In this thesis it is shown that if G is bipartite and jF(v)j dG(v) 2 for every v 2 V (G), then G is F-avoiding. The bound jF(v)j dG(v) 2 is best possible. For every graph G, we conjecture that if jF(v)j dG(v) 1 2 for every v 2 V (G), then G is F-avoiding. We also argue this conjecture; the best possibility and some partial solutions, e.g. for the complete graphs. For graph G, we say the set f(d+ i ; d i ); i = 1; : : : ; ng of...