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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D.F. MEXICO

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.

Keywords

ENG
kernel, kernel-perfect, critical kernel-imperfect

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Discussiones Mathematicae Graph Theory
2004/24/2
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Pages:
171-182
Main language of publication
English
Published
2004

DOI: 10.7151/dmgt.1223

Exact and natural sciences