14 problems

Ahn–Gollin–Huynh–Kwon conjecture. The upper bound can be improved to

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…

Let $G$ be a graph, and let $d$ be the prescribed distance separating cycles. Let $f(k)$ be the function in bounding the size of a vertex set meeting every collection of $k$ cycles…

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 $G$ be a graph with a fixed number of directed labellings, where a directed labelling assigns opposite group values to the two orientations of each edge, and call a cycle non-z…

Face-packing strengthening of Jones' Conjecture. For every planar graph $G$,

Let $l\geq 6$ be an integer, and let $\mathcal{C}_{\geq l}$ denote the class of cycles of length at least $l$. For a graph class $\mathcal{H}$, let…

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

Let $k$ be odd, and let a perfect packing of $k$-cycles in a regular tournament on $n$ vertices mean a packing of size $\lfloor n/k\rfloor$ when $k$ does not divide $n$. Cuckler's…