Rainbow graph splitting

Given an integer c, an edge colored graph G is said to be rainbow c-splittable if it can be decomposed into at most c vertex-disjoint monochromatic induced subgraphs of distinct colors. We provide a polynomial-time algorithm for deciding whether an edge-colored complete graph is rainbow c-splittable. For not necessarily complete graphs, we show that the problem is polynomial if c=2, whereas for c≥3 it is NP-complete even if the graph has maximum degree 2c−1. Finally, it remains NP-complete even for 2-edge colored graphs of maximum degree 7c−14.