Where can I find the formulation of the $k$-MST ($k$-minimum spanning tree) problem as (mixed) integer linear program based on Miller-Tucker-Zemlin subtour elimination constraints (MTZ)?
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Is this the formulation that you are looking for:
Min-degree constrained minimum spanning tree problem: New formulation via Miller–Tucker–Zemlin constraints
Source: http://yoksis.bilkent.edu.tr/pdf/files/10.1016-j.cor.2009.03.006.pdf