Towards a solution of the Holyer's problem
Let H be a fixed graph. We say that a graph G admits an H-decomposition if the set of edges of G can be partitioned into subsets generating graphs isomorphic to H. Denote by PH the problem of exsitence of an H-decomposition of a graph. The Holyer's problem is to classify the problems PH according to their computational complexities. In this paper we outline the proof of polynomiality of the problem PH for H being the union of s disjoint 2-edge paths. This case is believed to bear the main difficulties among so far uncovered cases.
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