Acyclic Subgraphs of Planar Digraphs
Name
Golowich-2015-Acyclic subgraphs.pdf
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223.83 KB
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Author(s)
Golowich, Noah
Rolnick, David S.
Date Issued
July 2015
Journal
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/4596
