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Kernels in a special class of digraphs

✍ Scribed by H. Galeana-Sánchez; Xueliang Li

Book ID
108316221
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
421 KB
Volume
178
Category
Article
ISSN
0012-365X

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## Abstract A vertex set __X__ of a digraph __D__ = (__V, A__) is a __kernel__ if __X__ is independent (i.e., all pairs of distinct vertices of __X__ are non‐adjacent) and for every __v__ ∈ __V__‐__X__ there exists __x__ ∈ __X__ such that __vx__ ∈ __A__. A vertex set __X__ of a digraph __D__ = (__V

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In this paper we present some results on the existence of /c-kernels and (k, [)-kernels in digraphs which generalize the following Theorem of P. Duchet [2]: "If every directed cycle of odd length in a digraph D has at least two symmetrical arcs, then D has a kernel.