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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2405.01767 |
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| _version_ | 1866913339955740672 |
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| author | Benítez-Bobadilla, Germán Galeana-Sánchez, Hortensia Hernández-Cruz, César |
| author_facet | Benítez-Bobadilla, Germán Galeana-Sánchez, Hortensia Hernández-Cruz, César |
| contents | A kernel in a digraph is an independent and absorbent subset of its vertex set. A digraph is critical kernel imperfect if it does not have a kernel, but every proper induced subdigraph does. In this article, we characterize asymmetrical $4$-quasi-transitive and $4$-transitive digraphs, as well as $2$-anti-transitive, and asymmetrical $4$-anti-transitive digraphs with bounded diameter, which are critical kernel imperfect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical Kernel Imperfectness in $4$-quasi-transitive and $4$-anti-transitive digraphs of small diameter Benítez-Bobadilla, Germán Galeana-Sánchez, Hortensia Hernández-Cruz, César Combinatorics 05C20, 05C69 A kernel in a digraph is an independent and absorbent subset of its vertex set. A digraph is critical kernel imperfect if it does not have a kernel, but every proper induced subdigraph does. In this article, we characterize asymmetrical $4$-quasi-transitive and $4$-transitive digraphs, as well as $2$-anti-transitive, and asymmetrical $4$-anti-transitive digraphs with bounded diameter, which are critical kernel imperfect. |
| title | Critical Kernel Imperfectness in $4$-quasi-transitive and $4$-anti-transitive digraphs of small diameter |
| topic | Combinatorics 05C20, 05C69 |
| url | https://arxiv.org/abs/2405.01767 |