Multigraph decomposition into stars and into multistars Original Research Article

We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixed star image: We present necessary and sufficient conditions for such a decomposition to exist where image and prove NP-completeness of the corresponding decision problem for any image. We also prove NP-completeness when the edge multiplicity function is not restricted either on the input G or on the fixed multistar H.