k-kernels in generalizations of transitive digraphs

• Autorzy: Hortensia Galeana-Sánchez , César Hernández-Cruz
• Języki publikacji: EN

Abstrakty

EN

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.
A (k,l)-kernel N of D is a k-independent set of vertices (if u,v ∈ N, u ≠ v, then d(u,v), d(v,u) ≥ k) and l-absorbent (if u ∈ V(D)-N then there exists v ∈ N such that d(u,v) ≤ l). A k-kernel is a (k,k-1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are generalizations of transitive digraphs. In this paper the following results are proved: Let D be a right-(left-) pretransitive strong digraph such that every directed triangle of D is symmetrical, then D has a k-kernel for every integer k ≥ 3; the result is also valid for non-strong digraphs in the right-pretransitive case. We also give a proof of the fact that every quasi-transitive digraph has a (k,l)-kernel for every integers k > l ≥ 3 or k = 3 and l = 2.

Słowa kluczowe

EN

digraph; kernel; (k,l)-kernel; k-kernel; transitive digraph; quasi-transitive digraph; right-pretransitive digraph; left-pretransitive digraph; pretransitive digraph

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 293-312

Daty

wydano

2011

otrzymano

2009-11-12

poprawiono

2010-08-23

zaakceptowano

2010-08-24

Twórcy

autor

Hortensia Galeana-Sánchez

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F., C.P. 04510, México

autor

César Hernández-Cruz

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F., C.P. 04510, México

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Identyfikatory

DOI

10.7151/dmgt.1546