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k minimum spanning trees

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this is for a small project at university:

we have to implement a java algorithm which produces a k-minimum spanning tree on a given graph (a minimum spanning tree with k nodes)
further we have to solve this with an algorithm based on branch and bound

my problem is to get useful heuristics for upper and lower bounds, to eliminate soon a lot of problems

my current approch works as following:
lower bound:
weight of currently fixed #e edges in graph + one adjacent edge to them + the weights of the k-1-e smallest edges

upper bound:
currently only set if a valid solution was found

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