5 problems

Let $V$ be a set with $|V|=n$, and let $\mathcal B,\mathcal C,\mathcal D\subset {V\choose 2}$ be RBT-free, meaning that no choice of one edge from each of the three families forms…

Let $(G,C)$ be an edge-colored graph on $n\geq 20$ vertices, and let $\delta^c(G)$ denote its minimum color degree. Hu–Li–Yang's conjecture. If … then $G$ contains two vertex-disjo…

Rainbow-triangle bound conjecture. For the existence of rainbow triangles in arc-colored regular tournaments, the bound

Hajnal's conjecture. There is an $\varepsilon>0$ such that every $3$-coloring of the edges of $K_n$ without a rainbow triangle contains a vertex set of order $n^{\varepsilon}$ whic…

Let $R_0$ denote the rainbow triangle pattern, and let $c_{3,R_0}(n)$ be the maximum number of colorings avoiding $R_0$ among graphs on $n$ vertices with three edge colors. Extrema…