5 problems

Seymour's conjecture. For positive integers $n$ and $k$ with $n\geq k+1$ and $k\geq2$, if

Kawarabayashi's conjecture. If

Let $l\geq 4$ be an integer, and let $k$ be the smallest integer greater than $2$ that does not divide $l$. Let $\delta^0(G)$ denote the minimum semi-degree of an oriented graph…

Dirac's conjecture. For all integers $1\leq d\leq k-1$ and $n$ divisible by $k$,

Let $k$, $n$, and $\delta$ be given. Define $G_p^{(k)}(n,\delta)$ by taking an interior set of $(k-1)(n-\delta)$ vertices carrying a complete balanced $(k-1)$-partite graph, an ext…