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On the minimum rainbow subgraph number of a graph
Schiermeyer, Ingo
We consider the Minimum Rainbow Subgraph problem (MRS): Given a graph ▫$G$▫, whose edges are coloured with ▫$p$▫ colours. Find a subgraph ▫$F \subseteq G$▫ of minimum order and with ▫$p$▫ edges such ...that each colour occurs exactly once. This problem is NP-hard and APX-hard. For a given graph ▫$G$▫ and an edge colouring ▫$c$▫ with ▫$p$▫ colours we define the rainbow subgraph number ▫$rs(G, c)$▫ to be the order of a minimum rainbow subgraph of ▫$G$▫ with size ▫$p$▫. In this paper we show lower and upper bounds for the rainbow subgraph number of a graph.
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