2 problems

Let $G$ be a finite simple graph. A Berge graph is a graph containing neither an odd hole nor the complement of an odd hole. A graph is basic if it belongs to one of the four class…

Let $T_1,\ldots,T_n$ be trees such that $T_k$ has $k$ vertices for every $k$ with $1\leq k\leq n$, and let $K_n$ be the complete graph on $n$ vertices. Gyárfás's tree-packing conje…