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98410 |
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|a Golowich, Noah
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|a Massachusetts Institute of Technology. Department of Mathematics
|e contributor
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|a Rolnick, David S.
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|a Rolnick, David S.
|e author
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|a Acyclic Subgraphs of Planar Digraphs
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|b European Mathematical Information Service (EMIS),
|c 2015-09-08T18:58:24Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/98410
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|a 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.
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|a en_US
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|a Article
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|t Electronic Journal of Combinatorics
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