Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Gomori-Hu inequality   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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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg