Rainbow graph splitting

Abstract 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 2 c − 1 . Finally, it remains NP-complete even for 2-edge colored graphs of maximum degree 7 c − 14 .

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