Max k-cut and judicious k-partitions
Alon, et al. (2003)  proved that every graph with a large cut has a bipartition in which each vertex class contains correspondingly few edges. We prove an analogous result for partitions into k ≥ 3 classes; along the way we prove a result for biased bipartitions. © 2010 Elsevier B.V. All rights reserved.
Bollobás, B., & Scott, A. (2010). Max k-cut and judicious k-partitions. Discrete Mathematics, 310 (15-16), 2126-2139. https://doi.org/10.1016/j.disc.2010.04.004