摘要：

This chapter discusses the evolution of path number of a graph in context of covering and packing in graphs. The concepts of packing and covering were explored in a lecture given in New York city, as a generalization of path number, arboricity, and several other graphical invariants. This approach suggested the definition of the linear arboricity of a graph, which has an interpretation in file structures. An alternative path-covering invariant of a graph can be defined as the minimum number of paths, unrestricted in that they are not necessarily line disjoint, needed to cover the lines of G. Although, several theorems are there for determining the path number of a graph, still there are some unsolved problems related to it and there are still no effective and convenient computer algorithms for determining the values of these five invariants for a given graph.

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