Kernel perfect and critical kernel imperfect digraphs structure
A kernel $N$ of a digraph $D$ is an independent set of vertices of $D$ such that for every $w \in V(D)-N$ 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. Minimal non-kernel perfect digraph are called critical kernel im...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3467/pdf |
| _version_ | 1797270388911112192 |
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| author | Hortensia Galeana-Sánchez Mucuy-Kak Guevara |
| author_facet | Hortensia Galeana-Sánchez Mucuy-Kak Guevara |
| author_sort | Hortensia Galeana-Sánchez |
| collection | DOAJ |
| description | A kernel $N$ of a digraph $D$ is an independent set of vertices of $D$ such that for every $w \in V(D)-N$ 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. Minimal non-kernel perfect digraph are called critical kernel imperfect digraph. If $F$ is a set of arcs of $D$, a semikernel modulo $F$, $S$ of $D$ is an independent set of vertices of $D$ such that for every $z \in V(D)- S$ for which there exists an $Sz-$arc of $D-F$, there also exists an $zS-$arc in $D$. In this talk some structural results concerning critical kernel imperfect and sufficient conditions for a digraph to be a critical kernel imperfect digraph are presented. |
| first_indexed | 2024-04-25T02:03:29Z |
| format | Article |
| id | doaj.art-ed03cb3188994d72b1c21a63e5c920b6 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:29Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-ed03cb3188994d72b1c21a63e5c920b62024-03-07T14:41:16ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34673467Kernel perfect and critical kernel imperfect digraphs structureHortensia Galeana-Sánchez0Mucuy-Kak Guevara1Instituto de MatematicasInstituto de MatematicasA kernel $N$ of a digraph $D$ is an independent set of vertices of $D$ such that for every $w \in V(D)-N$ 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. Minimal non-kernel perfect digraph are called critical kernel imperfect digraph. If $F$ is a set of arcs of $D$, a semikernel modulo $F$, $S$ of $D$ is an independent set of vertices of $D$ such that for every $z \in V(D)- S$ for which there exists an $Sz-$arc of $D-F$, there also exists an $zS-$arc in $D$. In this talk some structural results concerning critical kernel imperfect and sufficient conditions for a digraph to be a critical kernel imperfect digraph are presented.https://dmtcs.episciences.org/3467/pdfcritical kernel imperfect digraphkernelsemikernelsemikernel modulo fkernel perfect digraph[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| spellingShingle | Hortensia Galeana-Sánchez Mucuy-Kak Guevara Kernel perfect and critical kernel imperfect digraphs structure Discrete Mathematics & Theoretical Computer Science critical kernel imperfect digraph kernel semikernel semikernel modulo f kernel perfect digraph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| title | Kernel perfect and critical kernel imperfect digraphs structure |
| title_full | Kernel perfect and critical kernel imperfect digraphs structure |
| title_fullStr | Kernel perfect and critical kernel imperfect digraphs structure |
| title_full_unstemmed | Kernel perfect and critical kernel imperfect digraphs structure |
| title_short | Kernel perfect and critical kernel imperfect digraphs structure |
| title_sort | kernel perfect and critical kernel imperfect digraphs structure |
| topic | critical kernel imperfect digraph kernel semikernel semikernel modulo f kernel perfect digraph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-hc] computer science [cs]/human-computer interaction [cs.hc] |
| url | https://dmtcs.episciences.org/3467/pdf |
| work_keys_str_mv | AT hortensiagaleanasanchez kernelperfectandcriticalkernelimperfectdigraphsstructure AT mucuykakguevara kernelperfectandcriticalkernelimperfectdigraphsstructure |