Acyclic Subgraphs of Planar Digraphs
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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.
Date issued
2015-07Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Electronic Journal of Combinatorics
Publisher
European Mathematical Information Service (EMIS)
Citation
Golowich, Noah, and David Rolnick. "Acyclic Subgraphs of Planar Digraphs." The Electronic Journal of Combinatorics 22(3) (2015), #P3.7.
Version: Final published version
ISSN
1077-8926