Abstract
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 by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper, we proved that rc(G) ≤ 3(n + 1)/5 for all 3-connected graphs.
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Supported by NSFC and the Fundamental Research Funds for the Central Universities.
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Li, X., Shi, Y. Rainbow Connection in 3-Connected Graphs. Graphs and Combinatorics 29, 1471–1475 (2013). https://doi.org/10.1007/s00373-012-1204-9
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DOI: https://doi.org/10.1007/s00373-012-1204-9