Graphs on Surfaces

Abstract

Second edition. "A Chapman & Hall book." "Over the past fifty years, graph theory has been one of the most rapidly growing areas of mathematics. Since 1960, more than 10,000 di erent authors have published papers classi ed as graph theory by Math Reviews, and for the past decade, more than 1000 graph theory papers have been published each year. Not surprisingly, this Second Edition is about 450 pages longer than the First Edition, which appeared in 2004. This Handbook is intended to provide as comprehensive a view of graph theory as is feasible in a single volume. Many of our chapters survey areas that have large research communities, with hundreds of active mathematicians, and which could be developed into independent handbooks. The 89 contributors to this volume, 31 of whom are new to this edition, collectively represent perhaps as much as 90% or more of the main topics in pure and applied graph theory. Thirteen of the sections in the Second Edition cover newer topics that did not appear in the First Edition. Format In order to achieve this kind of comprehensiveness, we challenged our contributors to restrict their expository prose to a bare minimum, by adhering to the ready-reference style of the CRC Handbook series, which emphasizes quick accessibility for the non- expert. We thank the contributors for responding so well to this challenge. The 13 chapters of the Handbook are organized into 65 sections. Within each section, several major topics are presented. For each topic, there are lists of the essential de nitions and facts, accompanied by examples, tables, remarks, and in some cases, conjectures and open problems. Each section ends with a bibliography of references tied directly to that section"-- Introduction to graphs -- Graph representation -- Directed graphs -- Connectivity and traversability -- Colorings and related topics -- Algebraic graph theory -- Topological graph theory -- Analytic graph theory -- Graphical measurement -- Graphs in computer science -- Networks and flows -- Communication networks -- Natural science & processes.