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arXiv · 1311.2299

Rainbow Connection of Random Regular Graphs

Andrzej Dudek·Alan Frieze·Charalampos Tsourakakis
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Abstract

An edge colored graph $G$ is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection 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 work we study the rainbow connection of the random $r$-regular graph $G=G(n,r)$ of order $n$, where $r\ge 4$ is a constant. We prove that with probability tending to one as $n$ goes to infinity the rainbow connection of $G$ satisfies $rc(G)=O(\log n)$, which is best possible up to a hidden constant.

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Andrzej Dudek, Alan Frieze, Charalampos Tsourakakis. 2014-12-02. Rainbow Connection of Random Regular Graphs. https://arxiv.org/abs/1311.2299

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