6 problems

Hilton's conjecture. For every integer $\ell$ with $3\le \ell\le n$,

A graph is weakly pancyclic if the set of lengths of its cycles forms an interval. Brandt's conjecture. Every non-bipartite graph on $n$ vertices with more than … edges is weakly p…

A digraph $D$ has order $n\ge 3$. A pair of nonadjacent vertices is dominated if it has a common in-neighbor, and dominating if it has a common out-neighbor. Let $d(u)$ denote the…

Fujita and Magnant's conjecture. If

Manoussakis's conjecture. If, for every triple $x,y,z\in V(D)$ with $x$ nonadjacent to $y$, the inequalities

Let $n\geq 3$, let $k$ be an integer, and let $G$ be a graph of order $n$ with minimum degree … A $k$-edge colouring is a decomposition … where each $G_i$ is a spanning colour clas…