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arXiv · 1110.5772

Rainbow connection number of dense graphs

Xueliang Li·Mengmeng Liu·Ingo Schiermeyer
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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 $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper we show that $rc(G)\leq 3$, if $|E(G)|\geq {{n-2}\choose 2}+2$, and $rc(G)\leq 4$, if $|E(G)|\geq {{n-3}\choose 2}+3$. These bounds are sharp.

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Xueliang Li, Mengmeng Liu, Ingo Schiermeyer. 2011-10-26. Rainbow connection number of dense graphs. https://arxiv.org/abs/1110.5772

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