Build a transmuter for a given graph and a spanning tree of it

Give a graph and a spanning tree of it, a transmuter is an auxiliary graph derived from them and can speed up certain operations on original graph. It was invented by Tarjan:

Robert E. Tarjan. Applications of Path Compression on Balanced Trees. Journal of the ACM, 26(4):690–715, 1979.

Robert E. Tarjan. Sensitivity Analysis of Minimum Spanning Trees and Shortest Path Trees. Information Processing Letters, 14(1):30–33, 1982.

I find myself in need of a transmuter. Unfortunately I don't have access to both documents. Can someone know transmuter and / or have access to the documents elaborate a little bit about transmuter and the algorithm constructing it?

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unfortunately has no pdf link. see in case there are other papers that might help.

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