Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complementary cycles of any length in regular bipartite tournaments   Let $D$ be a $k$-regular bipartite tournament on $n$ vertices. We show that,
for every $p$ with $2 \le p \le n/2-2$, $D$ has a cycle $C$ of length $2p$ such
that $D \setminus C$ is hamiltonian unless $D$ is isomorphic to the special
digraph $F_{4k}$. This statement was conjectured by Manoussakis, Song and Zhang
[K. Zhang, Y. Manoussakis, and Z. Song. Complementary cycles containing a fixed
arc in diregular bipartite tournaments. Discrete Mathematics,
133(1-3):325--328,1994]. In the same paper, the conjecture was proved for $p=2$
and more recently Bai, Li and He gave a proof for $p=3$ [Y. Bai, H. Li, and W.
He. Complementary cycles in regular bipartite tournaments. Discrete
Mathematics, 333:14--27, 2014].

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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph