Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-disjoint properly edge-colored cycles in edge-colored complete
  graphs   It is conjectured that every edge-colored complete graph $G$ on $n$ vertices
satisfying $\Delta^{mon}(G)\leq n-3k+1$ contains $k$ vertex-disjoint properly
edge-colored cycles. We confirm this conjecture for $k=2$, prove several
additional weaker results for general $k$, and we establish structural
properties of possible minimum counterexamples to the conjecture. We also
reveal a close relationship between properly edge-colored cycles in
edge-colored complete graphs and directed cycles in multi-partite tournaments.
Using this relationship and our results on edge-colored complete graphs, we
obtain several partial solutions to a conjecture on disjoint cycles in directed
graphs due to Bermond and Thomassen.

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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: dg-ga