Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernels by properly colored paths in arc-colored digraphs   A {\em kernel by properly colored paths} of an arc-colored digraph $D$ is a
set $S$ of vertices of $D$ such that (i) no two vertices of $S$ are connected
by a properly colored directed path in $D$, and (ii) every vertex outside $S$
can reach $S$ by a properly colored directed path in $D$. In this paper, we
conjecture that every arc-colored digraph with all cycles properly colored has
such a kernel and verify the conjecture for unicyclic digraphs, semi-complete
digraphs and bipartite tournaments, respectively. Moreover, weaker conditions
for the latter two classes of digraphs are given.

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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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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: ao-sci
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The categories of this paper are: mtrl-th