ABSTRACT
One of the main treasures Paul Erdõs left us is his collection of problems, most of which are still open today. These problems are seeds that Paul sowed during his unceasing travels throughout the world during the past 60 years. As is well known, solutions to many of these problems (or often, attempts to solve them) have frequently led to substantial advances in the relevant areas, and on occasion, completely new branches within these disciplines (e.g., random graph theory, combinatorial set theory, and the probabilistic method). While Paul's interests (and therefore, problems) ranged over a wide spectrum of mathematics, it is our purpose in this monograph to collect many of his most interesting (in our opinion) problems in graph theory. Our interpretation of graph theory will be inclusive and will include hypergraphs and infinite graphs, for example. In this monograph, all problems placed within boxes are due to Erdõs (and his collaborators).
