Planar digraphs without large acyclic sets
Combinatorics
2016-06-15 v2 Discrete Mathematics
Abstract
Given a directed graph, an acyclic set is a set of vertices inducing a subgraph with no directed cycle. In this note we show that there exist oriented planar graphs of order for which the size of the maximum acyclic set is at most , for any . This disproves a conjecture of Harutyunyan and shows that a question of Albertson is best possible.
Cite
@article{arxiv.1504.06726,
title = {Planar digraphs without large acyclic sets},
author = {Kolja Knauer and Petru Valicov and Paul S. Wenger},
journal= {arXiv preprint arXiv:1504.06726},
year = {2016}
}
Comments
3 pages, 1 figure