Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Inductive Kernels of Graphs   It is well known that kernels in graphs are powerful and useful structures,
for instance in the theory of games. However, a kernel does not always exist
and Chv\'atal proved in 1973 that it is an NP-Complete problem to decide its
existence. We present here an alternative definition of kernels that uses an
inductive machinery : the inductive kernels. We prove that inductive kernels
always exist and a particular one can be constructed in quadratic time.
However, it is an NP-Complete problem to decide the existence of an inductive
kernel including (resp. excluding) some fixed vertex.

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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga