The Inductive Kernels of Graphs

Details The Inductive Kernels of Graphs The Inductive Kernels of Graphs

2007-10-08

arxiv.org/abs/0710.1551v1

Mathematics

Combinatorics

6 pages, 6 figures

Scientific paper

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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