# Spanning hypertree which connects the vertices as slowly as possible

I want to find a reference for the following problem or a similar problem for my paper. I found a greedy algorithm for this problem, but writing such an algorithm in a paper is not common in my area, and finding a reference is the best solution.

We have a connected hypergraph. We want to choose a list of hyperedges satisfying the following property: if you add the hyperedges to the empty hypergraph one by one, in each step the number of connected components reduces. At the beginning we have $$n$$ components, and at the end of these steps we have a single component. Suppose that in the $$i$$-th step, the number of components reduces by $$a_i$$. If we have $$t+1$$ steps, we want to minimize $$\max(a_1,a_2,\dots,a_t)$$.

I have an algorithm in which the complexity of each step is $$O(n^{a_i})$$. I would be glad to find a reference for this problem.