Bounds on the Number of Edges of Edge-minimal, Edge-maximal and   $l$-hypertrees
  In their paper, Bounds on the Number of Edges in Hypertrees, G.Y. Katona and P.G.N. Szab\'o introduced a new, natural definition of hypertrees in $k$-uniform hypergraphs and gave lower and upper bounds on the number of edges. They also defined edge-minimal, edge-maximal and $l$-hypertrees and proved an upper bound on the edge number of $l$-hypertrees.   In the present paper, we verify the asymptotic sharpness of the $\binom{n}{k-1}$ upper bound on the number of edges of $k$-uniform hypertrees given in the above mentioned paper. We also make an improvement on the upper bound of the edge number of $2$-hypertrees and give a general extension construction with its consequences.   We give lower and upper bounds on the maximal number of edges of $k$-uniform edge-minimal hypertrees and a lower bound on the number of edges of $k$-uniform edge-maximal hypertrees. In the former case, the sharp upper bound is conjectured to be asymptotically $\frac{1}{k-1}\binom{n}{2}$. 
P\'eter G. N. Szab\'o
math.CO