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arXiv · 1509.07256

The minimum size of graphs with given rainbow index

Thomas Y. H. Liu
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Abstract

The concept of $k$-rainbow index $rx_k(G)$ of a connected graph $G$, introduced by Chartrand, Okamoto and Zhang, is a natural generalization of the rainbow connection number. Let $t(n,k,\ell)$ denote the minimum size of a connected graph $G$ of order $n$ with $rx_k(G)\leq \ell$, where $2\leq \ell\leq n-1$ and $2\leq k\leq n$. In this paper, we obtain some exact values and some upper bounds for $t(n,k,\ell)$.

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Thomas Y. H. Liu. 2015-09-25. The minimum size of graphs with given rainbow index. https://arxiv.org/abs/1509.07256

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