6 problems

Burr–Erdős–Graham–Sós conjecture. For every integer $k\ge 3$,

Rainbow anti-Ramsey conjecture. The rainbow anti-Ramsey number for $(t+2)$ vertex-disjoint triangles satisfies

Let $n$ and $k$ be integers with $n\geq 3k$, let $kC_3$ be the vertex-disjoint union of $k$ triangles, and let $G_1(n,k),\ldots,G_4(n,k)$ be the four explicitly defined edge-colore…

Let $kC_3$ denote the union of $k$ vertex-disjoint copies of the triangle $C_3$. For a positive integer $n$, let $ar(n,kC_3)$ be the maximum number of colors in an edge-coloring of…

Let $K_{2n}$ be a complete graph with a proper edge-coloring using exactly $2n-1$ colors. A multicolored $2$-factor is a $2$-factor whose edges have pairwise distinct colors. The r…

Let $ar(n,k,s)$ be the least number of nonempty color classes in a coloring (partition) of ${[n]\choose k}$ that guarantees a rainbow $s$-matching, meaning $s$ pairwise disjoint…