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In this paper we consider the problem of finding the smallest number $q$ such that any graph $G$ of order $n$ admits a decomposition into edge disjoint copies of a fixed graph $H$ and single edges with at most $q$ elements. We solve the case when $H$ is the 5-cycle, the 5-cycle with a chord and any connected non-bipartite non-complete graph of order 4.doi:10.37236/1946 fatcat:n4jllowtabanfadcq5honfbu5q