Geodesic
Rainbow Connection Number of Graphs with Diameter 3
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 141-154.

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A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G is connected by a rainbow path. Let f(d) denote the minimum number such that rc(G) ≤ f(d) for each bridgeless graph G with diameter d. In this paper, we shall show that 7 ≤ f(3) ≤ 9.
Keywords: edge-coloring, rainbow path, rainbow connection number, diameter 
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Li, Hengzhe; Li, Xueliang; Sun, Yuefang. Rainbow Connection Number of Graphs with Diameter 3. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 141-154. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a10/

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