Variation to spanning tree called Group Spanning Tree

Suppose we have a complete graph with say 100 nodes. We divide the nodes in the graphs into groups for example 10 nodes in each group identified by color. We want to obtain an optimal spanning tree that operates under the constraint that at least one node will be present from each group. The resulting spanning tree can be called a group spanning tree. How to write an efficient algorithm for this making sure it is a tree(no cycles) and not looping over the entire node set on every pass to check presence of cycles and also making sure at least one node from each group is represented.