Max k-cut and the smallest eigenvalue
Let G be a graph of order n and size m, and let mck(G) be the maximum size of a k-cut of G. It is shown that mck(G)≤k-1/k(m-μmin(G)n/2), where μmin(G) is the smallest eigenvalue of the adjacency matrix of G. An infinite class of graphs forcing equality in this bound is constructed.
Linear Algebra and Its Applications
Nikiforov, V. (2016). Max k-cut and the smallest eigenvalue. Linear Algebra and Its Applications, 504, 462-467. https://doi.org/10.1016/j.laa.2016.04.019