Based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeat

This book is a tribute to Paul Erdos, the wandering mathematician once described as the prince of problem solvers and the absolute monarch or problem posers. It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erdos never had a home and never held a job. His home was a bag or two containing all his belongings and a record of the collective activities of the mathematical community. His job was one at which he excelled: identifying a...