There is a universal C such that every finite loopless k-edge-connected multigraph on at least two vertices has a spanning tree meeting each nontrivial cut in at most C/k times the number of original cut edges.
There is a universal C such that every finite loopless k-edge-connected multigraph on at least two vertices has a spanning tree meeting each nontrivial cut in at most C/k times the number of original cut edges.
There is a universal C such that every finite loopless k-edge-connected multigraph on at least two vertices has a spanning tree meeting each nontrivial cut in at most C/k times the number of original cut edges.
If correct, resolves the quantitative strong thin-tree conjecture at the necessary 1/k scale.
Does k-edge connectivity guarantee a spanning tree with O(1/k) occupancy on every cut?
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