Recently, it became apparent that a large number of the most
interesting structures and phenomena of the world can be described
by networks. To develop a mathematical theory of very large
networks is an important challenge. This book describes one recent
approach to this theory, the limit theory of graphs, which has
emerged over the last decade. The theory has rich connections with
other approaches to the study of large networks, such as ``property
testing'' in computer science and regularity partition in graph
theory. It has several applications in extremal graph theory,
including the exact formulations and partial answers to very
general questions, such as which problems in extremal graph theory
are decidable. It also has less obvious connections with other
parts of mathematics (classical and non-classical, like probability
theory, measure theory, tensor algebras, and semidefinite
optimization). This book explains many of these connections, first
at an informal level to emphasize the need to apply more advanced
mathematical methods, and then gives an exact development of the
theory of the algebraic theory of graph homomorphisms and of the
analytic theory of graph limits. This is an amazing book: readable,
deep, and lively. It sets out this emerging area, makes connections
between old classical graph theory and graph limits, and charts the
course of the future. --Persi Diaconis, Stanford University This
book is a comprehensive study of the active topic of graph limits
and an updated account of its present status. It is a beautiful
volume written by an outstanding mathematician who is also a great
expositor. --Noga Alon, Tel Aviv University, Israel Modern
combinatorics is by no means an isolated subject in mathematics,
but has many rich and interesting connections to almost every area
of mathematics and computer science. The research presented in
Lovasz's book exemplifies this phenomenon. This book presents a
wonderful opportunity for a student in combinatorics to explore
other fields of mathematics, or conversely for experts in other
areas of mathematics to become acquainted with some aspects of
graph theory. --Terence Tao, University of California, Los Angeles,
CA Laszlo Lovasz has written an admirable treatise on the exciting
new theory of graph limits and graph homomorphisms, an area of
great importance in the study of large networks. It is an
authoritative, masterful text that reflects Lovasz's position as
the main architect of this rapidly developing theory. The book is a
must for combinatorialists, network theorists, and theoretical
computer scientists alike. --Bela Bollobas, Cambridge University,
UK
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!