KP-digraphs and CKI-digraphs satisfying the k-Meyniel's condition

H. Galeana-Sánchez; V. Neumann-Lara

Discussiones Mathematicae Graph Theory (1996)

  • Volume: 16, Issue: 1, page 5-16
  • ISSN: 2083-5892

Abstract

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A digraph D is said to satisfy the k-Meyniel's condition if each odd directed cycle of D has at least k diagonals. The study of the k-Meyniel's condition has been a source of many interesting problems, questions and results in the development of Kernel Theory. In this paper we present a method to construct a large variety of kernel-perfect (resp. critical kernel-imperfect) digraphs which satisfy the k-Meyniel's condition.

How to cite

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H. Galeana-Sánchez, and V. Neumann-Lara. "KP-digraphs and CKI-digraphs satisfying the k-Meyniel's condition." Discussiones Mathematicae Graph Theory 16.1 (1996): 5-16. <http://eudml.org/doc/270225>.

@article{H1996,
abstract = { A digraph D is said to satisfy the k-Meyniel's condition if each odd directed cycle of D has at least k diagonals. The study of the k-Meyniel's condition has been a source of many interesting problems, questions and results in the development of Kernel Theory. In this paper we present a method to construct a large variety of kernel-perfect (resp. critical kernel-imperfect) digraphs which satisfy the k-Meyniel's condition. },
author = {H. Galeana-Sánchez, V. Neumann-Lara},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {digraph; kernel; independent set of vertices; absorbing set of vertices; kernel-perfect digraph; critical-kernel-imperfect digraph; τ-system; τ₁-system; indepedent kernel modulo Q; co-rooted tree; τ-construction; τ₁-construction; independent set; absorbing set; independent kernel; kernel-perfect; critical kernel-imperfect},
language = {eng},
number = {1},
pages = {5-16},
title = {KP-digraphs and CKI-digraphs satisfying the k-Meyniel's condition},
url = {http://eudml.org/doc/270225},
volume = {16},
year = {1996},
}

TY - JOUR
AU - H. Galeana-Sánchez
AU - V. Neumann-Lara
TI - KP-digraphs and CKI-digraphs satisfying the k-Meyniel's condition
JO - Discussiones Mathematicae Graph Theory
PY - 1996
VL - 16
IS - 1
SP - 5
EP - 16
AB - A digraph D is said to satisfy the k-Meyniel's condition if each odd directed cycle of D has at least k diagonals. The study of the k-Meyniel's condition has been a source of many interesting problems, questions and results in the development of Kernel Theory. In this paper we present a method to construct a large variety of kernel-perfect (resp. critical kernel-imperfect) digraphs which satisfy the k-Meyniel's condition.
LA - eng
KW - digraph; kernel; independent set of vertices; absorbing set of vertices; kernel-perfect digraph; critical-kernel-imperfect digraph; τ-system; τ₁-system; indepedent kernel modulo Q; co-rooted tree; τ-construction; τ₁-construction; independent set; absorbing set; independent kernel; kernel-perfect; critical kernel-imperfect
UR - http://eudml.org/doc/270225
ER -

References

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  1. [1] C. Berge, Graphs (North-Holland, Amsterdam, 1985). 
  2. [2] P. Duchet and H. Meyniel, A note on kernel-critical digraphs, Discrete Math. 33 (1981) 103-105, doi: 10.1016/0012-365X(81)90264-8. Zbl0456.05032
  3. [3] P. Duchet and H. Meyniel, Une generalization du theoreme de Richarson sur l'existence de noyoux dans les graphes orientes, Discrete Math. 43 (1983) 21-27, doi: 10.1016/0012-365X(83)90017-1. Zbl0502.05027
  4. [4] P. Duchet, A suffiecient condition for a digraph to be kernel-perfect, J. Graph Theory 11 (1987) 81-81, doi: 10.1002/jgt.3190110112. Zbl0607.05036
  5. [5] H. Galeana-Sánchez and V. Neumann-Lara, On kernels and semikernels of digraphs, Discrete Math. 48 (1984) 67-76, doi: 10.1016/0012-365X(84)90131-6. Zbl0529.05024
  6. [6] H. Galeana-Sánchez and V. Neumann-Lara, On kernel-perfect critical digraphs, Discrete Math. 59 (1986) 257-265, doi: 10.1016/0012-365X(86)90172-X. Zbl0593.05034
  7. [7] H. Galeana-Sánchez and V. Neumann-Lara, Extending kernel perfect digraphs to kernel perfect critical digraphs, Discrete Math. 94 (1991) 181-187, doi: 10.1016/0012-365X(91)90023-U. Zbl0748.05060
  8. [8] H. Jacob, Etude Theorique du Noyau d'un graphe, These, Universite Pierre et Marie Curie, Paris VI, 1979. 
  9. [9] V. Neumann-Lara, Seminúcleos de una digráfica, Anales del Instituto de Matemáticas 11 (1971) UNAM. 

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