7 problems

Caro's conjecture. For every odd $q\ge5$,

Let $G$ be a graph on $n$ vertices such that $3\mid e(G)$, and let $R(G,\mathbb{Z}_3)$ denote its zero-sum Ramsey number. Universal zero-sum Ramsey conjecture. … with equality if a…

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…

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.

MMS star conjecture. For any nonnegative weighting, the largest MMS set has size at least the size of a star.