3 problems

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…

Let $k\geq 1$ and let $T_n,T_{n-1},\dots,T_{n-k+1}$ be trees, where $T_{n-j}$ has $n-j$ vertices. The trees pack into $K_n$ when they can be found as pairwise edge-disjoint subgrap…

A tree degree sequence is a list of positive integers whose sum is $2n-2$; a realization is a graph with exactly those vertex degrees. Let $D_1,D_2,\ldots,D_k$ be tree degree seque…