3 problems

Let $G$ be a planar graph, and let $k$ be a nonnegative integer. Pairwise disjoint cycles in $G$ have no common vertices. Jones' conjecture. If $G$ contains no more than $k$ pairwi…

Younger’s conjecture. For every directed graph $D$, there exists a function $f$ such that, if $D$ does not contain $k$ disjoint cycles, then $D$ has a feedback vertex set of size a…

A cycle packing problem is considered in which the goal is to identify the maximum number of disjoint cycles, and let $n$ denote the number of vertices. The cycle-packing approxima…