Geodesic
Rainbow Connection Number of Dense Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 603-611 Cet article a éte moissonné depuis la source Library of Science

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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)| ≥n-22 + 2, and rc(G) ≤ 4 if |E(G)| ≥n-32 + 3. These bounds are sharp.
Keywords: edge-colored graph, rainbow coloring, rainbow connection number 
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Li, Xueliang; Liu, Mengmeng; Schiermeyer, Ingo. Rainbow Connection Number of Dense Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 603-611. http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a9/

[1] J.A. Bondy and U.S.R. Murty, Graph Theory (GTM 244, Springer, 2008).

[2] G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang, Rainbow connection in graphs, Math. Bohem. 133 (2008) 85-98.

[3] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.

[4] A. Kemnitz and I. Schiermeyer, Graphs with rainbow connection number two, Disscuss. Math. Graph Theory 31 (2011) 313-320. doi:10.7151/dmgt.1547

[5] X. Li and Y. Sun, Rainbow Connections of Graphs (SpringerBriefs in Math., Springer, New York, 2012). doi:10.1007/978-1-4614-3119-0