Abstract
In a inear forest, each component is a path. The linear arboricity ≡(G) of a graph G is defined in Harary [8] as the minimum number of linear forests whose union is G. This invariant first arose in a study [10] of information retrieval in file systems. A quite similar covering invariant which is well known to the linear arboricity is the arboricity of a graph, which is defined as the minimum number of forests whose union is G. Nash-Williams [11] determined the arboricity of any graph, however only few results on the linear arboricity are known. We shall present these discoveries and an open problem on this new invariant.
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