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arXiv · 2502.02482

Revisiting classical results on kernels in digraphs

Hélène Langlois·Frédéric Meunier
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Abstract

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.

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Hélène Langlois, Frédéric Meunier. 2025-02-04. Revisiting classical results on kernels in digraphs. https://arxiv.org/abs/2502.02482

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