- Tytuł:
- A sufficient condition for the existence of k-kernels in digraphs
- Autorzy:
-
Galeana-Sánchez, H.
Rincón-Mejía, H. - Powiązania:
- https://bibliotekanauki.pl/articles/744223.pdf
- Data publikacji:
- 1998
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
digraph
kernel
k-kernel - Opis:
-
In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with l(γ) ≢ 0 (mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has four short chords. Then D has a k-kernel.
This result generalizes some previous results on the existence of kernels and k-kernels in digraphs. In particular, it generalizes the following Theorem of M. Kwaśnik [5]: Let D be a strongly connected digraph, if every directed cycle of D has length ≡ 0 (mod k), k ≥ 2. Then D has a k-kernel. - Źródło:
-
Discussiones Mathematicae Graph Theory; 1998, 18, 2; 197-204
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł