2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 257262
author:  Hortensia GaleanaSánchez and MucuyKak Guevara 

title:  Semikernels modulo F in Digraphs 
keywords:  kernel, semikernel, semikernel modulo F, kernel perfect digraph, critical kernel imperfect digraph 
abstract: 
A kernel
N
of a digraph
D
is an independent set of vertices of
D
such that for every
w∈V(D)N
there exists an arc from
w
to
N
. If every induced subdigraph of
D
has a kernel,
D
is said to be a kernel perfect digraph. Minimal
nonkernel perfect digraph are called critical kernel
imperfect digraph. If
F
is a set of arcs of
D
, a semikernel modulo
F
,
S
of
D
is an independent set of vertices of
D
such that for every
z∈V(D) S
for which there exists an
Sz
arc of
DF
, there also exists an
zS
arc in
D
. In this talk some structural results concerning
critical kernel imperfect and sufficient conditions for a
digraph to be a critical kernel imperfect digraph are
presented.

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reference:  Hortensia GaleanaSánchez and MucuyKak Guevara (2005), Semikernels modulo F in Digraphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 257262 
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