A lower bound for the Laplacian eigenvalues of a graph—Proof of a conjecture by Guo

We show that if μj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1⩽j⩽n) of a connected graph Γ on n vertices, then μj⩾dj-j+2(1⩽j⩽n-1). This settles a conjecture due to Guo.