4 problems

Let $T$ be a regular tournament on $n$ vertices, where $n$ is odd. A collection of directed triangles is pairwise edge-disjoint if no directed edge belongs to more than one triangl…

Let $K_n$ be the complete graph on $n$ vertices with its edges coloured red and blue. A collection of triangles is pairwise edge-disjoint if no edge occurs in more than one triangl…

Let $K_n$ be the complete graph on $n$ vertices whose edges are coloured with two colours. A collection of triangles is pairwise edge-disjoint if no edge belongs to more than one t…

Let $\varepsilon>0$. A graph is globally $m$-bounded if no colour is used on more than $m$ edges, and a forest of order $k$ has $k$ edges. Rainbow forest packing conjecture. There…