6 problems

Let $T$ be a tree on $n \equiv 1 \pmod{3}$ vertices. Caro's conjecture. … This conjecture extends the understanding of zero-sum Ramsey numbers from $\mathbb{Z}_2$ to the next cycli…

Let $m \geq k \geq 2$ be integers such that $k \mid m$, and let $T_{m+1}$ be a tree on $n=m+1$ vertices. Let $G$ be a graph with minimum degree at least $n+k-2$. Caro–Roditty conje…

Pardey–Rautenbach conjecture. If $c\colon E(K_{2kn})\to [k]$ is colour-balanced, then there is a perfect matching $M$ of $K_{2kn}$ such that

Let $K_n$ be a complete graph of order $n$, and let $c:E(K_n)\to \{-1,1\}$ be a zero-sum labeling satisfying … Let $F$ be a spanning forest of $K_n$ with maximum degree $\Delta$. M…

Strict MMS star conjecture for order 7. Any Latin square of order $7$ has the strict MMS star property.

MMS star conjecture for order 6. Any Latin square of order $6$ has the MMS star property.