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I am looking for information about graphs, that are the union of $k$ edge-disjoint spanning trees "EDSP" of finite symmetric graphs. I am especially interested in theorems and algorithms related to characterizing and/or determining $k$-tuples of EDSPs in weighted graphs with minimal weight sum.

The problem I actually need to solve, ist to determine a weight-optimal bridgeless cactus graph in a complete symmetric graph; my idea is to take a weight-optimal, edge-disjoint pair of spanning trees and repeatedly remove the longest edge, that belongs to more than one cycle. I'm not sure, if the idea is right, but its at least a starting point.

Question: where can I find information about the theory and algorithms related to unions of edge-disjoint spanning trees?

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