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New classes of critical kernel-imperfect digraphs

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Galeana-Sánchez H., Neumann-Lara V.

Discussiones Mathematicae Graph Theory

1998

tom 18

nr 1

85-89

A kernel of a digraph D is a subset N ⊆ V(D) which is both independent and absorbing. When every induced subdigraph of D has a kernel, the digraph D is said to be kernel-perfect. We say that D is a critical kernel-imperfect digraph if D does not have a kernel but every proper induced subdigraph of D does have at least one. Although many classes of critical kernel-imperfect-digraphs have been constructed, all of them are digraphs such that the block-cutpoint tree of its asymmetrical part is a path. The aim of the paper is to construct critical kernel-imperfect digraphs of a special structure, a general method is developed which permits to build critical kernel-imperfect-digraphs whose asymmetrical part has a prescribed block-cutpoint tree. Specially, any directed cactus (an asymmetrical digraph all of whose blocks are directed cycles) whose blocks are directed cycles of length at least 5 is the asymmetrical part of some critical kernel-imperfect-digraph.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Galeana-Sánchez H.

1 Neumann-Lara V.

1 1998

Wyniki wyszukiwania

New classes of critical kernel-imperfect digraphs