On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ

Magdalena Kucharska; Maria Kwaśnik

Discussiones Mathematicae Graph Theory (2001)

  • Volume: 21, Issue: 1, page 95-109
  • ISSN: 2083-5892

Abstract

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The concept of (k,l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [4] proved a sufficient condition for a digraph to have a (k,l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k,l)-kernel. We restrict our attention to special superdigraphs of digraphs Pₘ and Cₘ.

How to cite

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Magdalena Kucharska, and Maria Kwaśnik. "On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ." Discussiones Mathematicae Graph Theory 21.1 (2001): 95-109. <http://eudml.org/doc/270606>.

@article{MagdalenaKucharska2001,
abstract = {The concept of (k,l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [4] proved a sufficient condition for a digraph to have a (k,l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k,l)-kernel. We restrict our attention to special superdigraphs of digraphs Pₘ and Cₘ.},
author = {Magdalena Kucharska, Maria Kwaśnik},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {kernel; semikernel; (k,l)-kernel},
language = {eng},
number = {1},
pages = {95-109},
title = {On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ},
url = {http://eudml.org/doc/270606},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Magdalena Kucharska
AU - Maria Kwaśnik
TI - On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 1
SP - 95
EP - 109
AB - The concept of (k,l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [4] proved a sufficient condition for a digraph to have a (k,l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k,l)-kernel. We restrict our attention to special superdigraphs of digraphs Pₘ and Cₘ.
LA - eng
KW - kernel; semikernel; (k,l)-kernel
UR - http://eudml.org/doc/270606
ER -

References

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  1. [1] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1976). 
  2. [2] M. Kwaśnik, The generalization of Richardson theorem, Discuss. Math. IV (1981) 11-14. Zbl0509.05048
  3. [3] V. Neumann-Lara, Seminúcleas en una digráfica, Anales del Instituto de Matemáticas de la Universidad Nacional Autónoma de México 11 (1971) 55-62. 
  4. [4] H. Galeana-Sánchez, On the existence of (k,l)-kernels in digraphs, Discrete Math. 85 (1990) 99-102, doi: 10.1016/0012-365X(90)90167-G. 
  5. [5] I. Włoch, Minimal Hamiltonian graphs having a strong (k,k-2)-kei>, Zeszyty Naukowe Politechniki Rzeszowskiej No. 127 (1994) 93-98. Zbl0853.05054

Citations in EuDML Documents

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  1. Hortensia Galeana-Sánchez, Ricardo Gómez, (k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings
  2. Hortensia Galeana-Sánchez, César Hernández-Cruz, Cyclically k-partite digraphs and k-kernels
  3. Hortensia Galeana-Sánchez, César Hernández-Cruz, k-kernels in generalizations of transitive digraphs
  4. Magdalena Kucharska, On (k,l)-kernel perfectness of special classes of digraphs
  5. Pietra Delgado-Escalante, Hortensia Galeana-Sánchez, Kernels and cycles' subdivisions in arc-colored tournaments
  6. Pietra Delgado-Escalante, Hortensia Galeana-Sánchez, On monochromatic paths and bicolored subdigraphs in arc-colored tournaments
  7. H. Galeana-Sánchez, C. Hernández-Cruz, On the Existence of (k,l)-Kernels in Infinite Digraphs: A Survey

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