The Inductive Kernels of Graphs
Combinatorics
2007-10-09 v1 Optimization and Control
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 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.
Cite
@article{arxiv.0710.1551,
title = {The Inductive Kernels of Graphs},
author = {Serge Burckel},
journal= {arXiv preprint arXiv:0710.1551},
year = {2007}
}
Comments
6 pages, 6 figures