example: I need to rewire the computer network at school, using as little cable as possible. So I create an MST of the existing routes. Now there is a problem, I am not allowed to buy additional routers. And the current routers (vertexes) are limited by the number of ports for further connection 2, 4,6 or 10.
How do I calculate my minimum spanning tree for this problem?
Even in the special case where the maximum number of visits is fixed, this problem is NP-hard. However there are good approximation algorithms.
See https://en.wikipedia.org/wiki/Degree-constrained_spanning_tree for more.