The $k$-section width and the Max-Cut for the configuration model are shown to exhibit phase transitions according to the values of certain parameters of the asymptotic degree distribution. These transitions mirror those observed on Erdős-Rényi random graphs, established by Luczak and McDiarmid (2001), and Coppersmith et al. (2004), respectively.
"Phase transitions of extremal cuts for the configuration model." Electron. J. Probab. 22 1 - 29, 2017. https://doi.org/10.1214/17-EJP109