Revisiting classical results on kernels in digraphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910814157406208 |
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| author | Langlois, Hélène Meunier, Frédéric |
| author_facet | Langlois, Hélène Meunier, Frédéric |
| contents | In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence is a key theoretical challenge. In this work, we revisit and generalize a few classical results of this sort, especially the Sands--Sauer--Woodrow theorem and the Galeana-Sánchez--Neumann-Lara theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting classical results on kernels in digraphs Langlois, Hélène Meunier, Frédéric Combinatorics Discrete Mathematics G.2.2 In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence is a key theoretical challenge. In this work, we revisit and generalize a few classical results of this sort, especially the Sands--Sauer--Woodrow theorem and the Galeana-Sánchez--Neumann-Lara theorem. |
| title | Revisiting classical results on kernels in digraphs |
| topic | Combinatorics Discrete Mathematics G.2.2 |
| url | https://arxiv.org/abs/2502.02482 |