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Journal Articles Journal of Multiple-Valued Logic and Soft Computing Year : 2016

Inductive Kernels of Graphs

Abstract

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 Chvátal 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 linear 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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Dates and versions

hal-01479612 , version 1 (28-02-2017)

Identifiers

  • HAL Id : hal-01479612 , version 1

Cite

Serge Burckel. Inductive Kernels of Graphs. Journal of Multiple-Valued Logic and Soft Computing, 2016, 27 (2/3), pp.175-181. ⟨hal-01479612⟩
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