Graphs On Surfaces

Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory bas numerous applications in almost every field of science and has attracted new interest because of its relevance to, such technological problems as computer and telephone networking and, of course, the Internet. In this new book in the Johns Hopkins Studies in the Mathematical Sciences series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. "This is a long-awaited book by two of the most powerful practitioners in the field. There is nothing else like it, and it will remain the definitive book on the subject for many, many years to come." -Thomas Tucker, Colgate University, co-author of Topological Graph Theory