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arXiv · 1211.2389

On the Gomori-Hu inequality

E. Petrov·O. Dovgoshey
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Abstract

It was proved by Gomori and Hu in 1961 that for every finite nonempty ultrametric space $(X,d)$ the following inequality $|\Sp(X)|\leqslant |X|-1$ holds with $\Sp(X)=\{d(x,y):x,y \in X, x\neq y\}$. We characterize the spaces $X$, for which the equality in this inequality is attained by the structural properties of some graphs and show that the set of isometric types of such $X$ is dense in the Gromov-Hausdorff space of the compact ultrametric spaces.

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E. Petrov, O. Dovgoshey. 2012-11-11. On the Gomori-Hu inequality. https://arxiv.org/abs/1211.2389

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