8 problems

Let $\Sigma$ be a signed graph. Denote by $p^-(\Sigma)$ the maximum number of edge-disjoint negative cycles, by $l(\Sigma)$ its frustration index, and by $p(\Sigma)$ the maximum nu…

For a positive integer $d$, a distance-$d$ packing of cycles in a graph $G$ is a set of cycles such that no path of length at most $d$ joins two distinct cycles. For a vertex set…

Asymptotic directed-cycle packing and covering conjecture. For all sufficiently large $n$, every $n$-vertex directed graph $D$ satisfies

Let $c,k$ be integers with $c\geq 2$ and $k\geq 1$. For an integer $r\geq 0$, an $r$-chorded cycle is a cycle with $r$ chords. Gould, Horn and Magnant's conjecture. Every graph $G$…

Even average-degree cycle-packing conjecture. If $G$ has average degree at least

Hwang's even-cycle packing conjecture. If $G$ has at least $rk$ vertices and minimum degree at least

Hwang's odd-cycle packing conjecture. If $G$ has at least $rk$ vertices and minimum degree at least

Long-cycle packing conjecture. Every graph with minimum degree at least