Small Feedback Vertex Sets in Planar Digraphs

Louis Esperet, Laetitia Lemoine, Frédéric Maffray


Let $G$ be a directed planar graph on $n$ vertices, with no directed cycle of length less than $g\ge 4$. We prove that $G$ contains a set $X$ of vertices such that $G-X$ has no directed cycle, and $|X|\le \tfrac{5n-5}9$ if $g=4$, $|X|\le \tfrac{2n-5}4$ if $g=5$, and $|X|\le \tfrac{2n-6}{g}$ if $g\ge 6$. This improves recent results of Golowich and Rolnick.


Planar Digraphs; Digirth; Feedback Vertex Sets

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