Eigenvalue inequalities for graphs and convex subgraphs (Q1389072)

For an induced subgraph of a graph the authors show a lower bound for its Neumann eigenvalue in terms of the heat kernel and vertex degrees. This yields a lower bound of eigenvalues for convex subgraphs of a Riemannian manifold. This bound is useful for bounding the rates of convergence for several random walk problems, which, in turn, finds applications in many enumeration problems.