Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of complete interval tournaments   Let $a, b$ and $n$ be nonnegative integers $(b \geq a, \ b > 0, \ n \geq 1)$,
$\mathcal{G}_n(a,b)$ be a multigraph on $n$ vertices in which any pair of
vertices is connected with at least $a$ and at most $b$ edges and \textbf{v =}
$(v_1, v_2, ..., v_n)$ be a vector containing $n$ nonnegative integers. We give
a necessary and sufficient condition for the existence of such orientation of
the edges of $\mathcal{G}_n(a,b)$, that the resulted out-degree vector equals
to \textbf{v}. We describe a reconstruction algorithm. In worst case checking
of \textbf{v} requires $\Theta(n)$ time and the reconstruction algorithm works
in $O(bn^3)$ time. Theorems of H. G. Landau (1953) and J. W. Moon (1963) on the
score sequences of tournaments are special cases $b = a = 1$ resp. $b = a \geq
1$ of our result.

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The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess