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- W1778531840 abstract "An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on $n$ vertices without directed 2-cycles possesses an acyclic set of size at least $3n/5$. We prove this conjecture for digraphs where every directed cycle has length at least 8. More generally, if $g$ is the length of the shortest directed cycle, we show that there exists an acyclic set of size at least $(1 - 3/g)n$." @default.
- W1778531840 created "2016-06-24" @default.
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- W1778531840 date "2015-07-01" @default.
- W1778531840 modified "2023-09-26" @default.
- W1778531840 title "Acyclic Subgraphs of Planar Digraphs" @default.
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- W1778531840 doi "https://doi.org/10.37236/4596" @default.
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