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.
@article{bwmeta1.element.doi-10_7151_dmgt_1920,
author = {Hengzhe Li and Xueliang Li and Yuefang Sun},
title = {Rainbow Connection Number of Graphs with Diameter 3},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {141-154},
zbl = {1354.05050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1920}
}
Hengzhe Li; Xueliang Li; Yuefang Sun. Rainbow Connection Number of Graphs with Diameter 3. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 141-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1920/