Abstract
Merker and Postle showed that any graph that can be decomposed into a forest and a star forest has a decomposition into two forests with diameter at most 18. Using this result, they proved any planar graph of girth at least 6 has two edge-disjoint 1819-thin spanning trees. By using a simpler version of their techniques, given a graph that can be decomposed into a forest and a matching, in polynomial time, we decompose the graph into two forests with diameter at most 12. Using this result, we are able to show that any 8-edge-connected planar graph has two edge-disjoint 1213-thin spanning trees.
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