# Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 2, page 171-182
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez. "Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel." Discussiones Mathematicae Graph Theory 24.2 (2004): 171-182. <http://eudml.org/doc/270195>.

@article{HortensiaGaleana2004,

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. 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.},

author = {Hortensia Galeana-Sánchez},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {kernel; kernel-perfect; critical kernel-imperfect; digraph},

language = {eng},

number = {2},

pages = {171-182},

title = {Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel},

url = {http://eudml.org/doc/270195},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

TI - Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 2

SP - 171

EP - 182

AB - 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.

LA - eng

KW - kernel; kernel-perfect; critical kernel-imperfect; digraph

UR - http://eudml.org/doc/270195

ER -

## References

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