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 thatmck(G)≤k−1k(m−μmin(G)n2),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.