Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 lor 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. #R##N#In the present paper,  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.  also make an improvement on the upper bound of the edge number of $2$-hypertrees and give a general extension construction with its consequences. #R##N# give lor and upper bounds on the maximal number of edges of $k$-uniform edge-minimal hypertrees and a lor 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 $\frac{1}{k-1}\binom{n}{2}$.
['Péter G. N. Szabó']
I am writing a research paper on a idea Bounds on the number of edges of edge-minimal, edge-maximal and l-hypertrees
[{"from": "human", "value": "I am writing a research paper on a idea Bounds on the number of edges of edge-minimal, edge-maximal and l-hypertrees"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 lor 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. #R##N#In the present paper,  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.  also make an improvement on the upper bound of the edge number of $2$-hypertrees and give a general extension construction with its consequences. #R##N# give lor and upper bounds on the maximal number of edges of $k$-uniform edge-minimal hypertrees and a lor 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 $\\frac{1}{k-1}\\binom{n}{2}$."}]