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In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths . We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when
(i) either H does not have incident multiple edges or
(ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.
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