A lower bound on the order of the largest induced forest in planar graphs with high girth

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 $\frac{n+2}{3}$.

12 pages, 6 figures. arXiv admin note: text overlap with arXiv:1409.1348

References in corpus (1)

• Large induced forests in planar graphs with girth 4 or 5