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. In this paper I investigate some sufficient conditions for a digraph to have a kernel by asking for the existence of certain diagonals or symmetrical arcs in each odd directed cycle whose length is at most 2α(D)+1, where α(D) is the maximum cardinality of an independent vertex set of D. Previous results are generalized.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1223,
author = {Hortensia Galeana-S\'anchez},
title = {Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel},
journal = {Discussiones Mathematicae Graph Theory},
volume = {24},
year = {2004},
pages = {171-182},
zbl = {1063.05059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1223}
}
Hortensia Galeana-Sánchez. Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 171-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1223/
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