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An edge-coloured connected graph G is rainbow connected if each two vertices are connected by a path whose edges have distinct colours. If such a colouring uses k colours then G is called k-rainbow connected. The rainbow connection number of G, denoted by rc(G), is the minimum k such that G is k-rainbow connected. Even the problem to decide whether rc(G)=2 is NP-complete. It has been shown that if...
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