Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-disjoint cycles in tournaments   The Bermond-Thomassen conjecture states that, for any positive integer $r$, a
digraph of minimum out-degree at least $2r-1$ contains at least $r$
vertex-disjoint directed cycles. Bessy, Sereni and Lichiardopol proved that a
regular tournament $T$ of minimum degree $2r-1$ contains at least $r$
vertex-disjoint directed cycles, which shows that the above conjecture is true
for tournaments. After that, Lichiardopol improved this result by showing that
a $2r-1$-regular tournament contains at least $\frac{7}{6}r-\frac{7}{3}$
vertex-disjoint directed cycles. In this paper, we will extend the result to
tournaments with minimum out-degree at least $2r-1$ by proving a more general
result.

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The categories of this paper are: nlin
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat