Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving the kernel perfect problem by (simple) forbidden subdigraphs for
  digraphs in some families of generalized tournaments and generalized
  bipartite tournaments   A digraph such that every proper induced subdigraph has a kernel is said to
be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI
for short) resp.) if the digraph has a kernel (does not have a kernel resp.).
The unique CKI-tournament is $\overrightarrow{C}_3$ and the unique
KP-tournaments are the transitive tournaments, however bipartite tournaments
are KP. In this paper we characterize the CKI- and KP-digraphs for the
following families of digraphs: locally in-/out-semicomplete, asymmetric
arc-locally in-/out-semicomplete, asymmetric $3$-quasi-transitive and
asymmetric $3$-anti-quasi-transitive $TT_3$-free and we state that the problem
of determining whether a digraph of one of these families is CKI is polynomial,
giving a solution to a problem closely related to the following conjecture
posted by Bang-Jensen in 1998: the kernel problem is polynomially solvable for
locally in-semicomplete digraphs.

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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg