On the minimum rainbow subgraph number of a graph

Abstract

We consider the MINIMUM RAINBOW SUBGRAPH problem (MRS): Given a graph G whose edges are coloured with p colours. Find a subgraph F 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 will show lower and upper bounds for the rainbow subgraph number of a graph. Copyright © 2013 DMFA Slovenije.