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.

Publication Title

Linear Algebra and Its Applications