# Gomory-Hu Trees in Quadratic Time

@article{Zhang2021GomoryHuTI, title={Gomory-Hu Trees in Quadratic Time}, author={Tianyi Zhang}, journal={ArXiv}, year={2021}, volume={abs/2112.01042} }

Gomory-Hu tree [Gomory and Hu, 1961] is a succinct representation of pairwise minimum cuts in an undirected graph. When the input graph has general edge weights, classic algorithms need at least cubic running time to compute a Gomory-Hu tree. Very recently, the authors of [AKL+, arXiv v1, 2021] have improved the running time to Õ(n) which breaks the cubic barrier for the first time. In this paper, we refine their approach and improve the running time to Õ(n). This quadratic upper bound is also…

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