Emergent Mind
A lower bound on the order of the largest induced forest in planar graphs with high girth
(1504.01949)
Published Apr 8, 2015
in
cs.DM
and
math.CO
Abstract
We give here new upper bounds on the size of a smallest feedback vertex set in planar graphs with high girth. In particular, we prove that a planar graph with girth $g$ and size $m$ has a feedback vertex set of size at most $\frac{4m}{3g}$, improving the trivial bound of $\frac{2m}{g}$. We also prove that every $2$-connected graph with maximum degree $3$ and order $n$ has a feedback vertex set of size at most $\frac{n+2}{3}$.
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