An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ [...] + 2, and rc(G) ≤ 4 if |E(G)| ≥ [...] + 3. These bounds are sharp.
@article{bwmeta1.element.doi-10_7151_dmgt_1692,
author = {Xueliang Li and Mengmeng Liu and Ingo Schiermeyer},
title = {Rainbow Connection Number of Dense Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {603-611},
zbl = {1275.05022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1692}
}
Xueliang Li; Mengmeng Liu; Ingo Schiermeyer. Rainbow Connection Number of Dense Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 603-611. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1692/
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