Let (G) be the largest eigenvalue of the adjacency matrix of a graph G: We show that if G is Kp+1-free then (G) r 2 p 1 p e (G): This inequality was ...rst conjectured by Edwards ...
We study a model motivated by the minesweeper game. In this model one starts with percolation of mines on the sites of the lattice Zd , and then tries to find an infinite path of ...
The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the varianc...