Minimum Rainbow $H$-Decompositions of Graphs

Abstract: Given graphs $G$ and $H$, we consider the problem of decomposing a properly edge-colored graph $G$ into few parts consisting of rainbow copies of $H$ and single edges. We establish a close relation to the previously studied problem of minimum $H$-decompositions, where an edge coloring does not matter and one is merely interested in decomposing graphs into copies of $H$ and single edges.