Improved guarantees for vertex sparsification in planar graphs
G. Goranci, M. Henzinger, P. Peng, SIAM Journal on Discrete Mathematics 34 (2020) 130–162.

Bounded-degree spanning trees in randomly perturbed graphs
M. Krivelevich, M.A. Kwan, B. Sudakov, SIAM Journal on Discrete Mathematics 31 (2017) 155–171.