Convergence of sequences of simple graphs
Title | Convergence of sequences of simple graphs PDF eBook |
Author | Jack Wyndall Rogers |
Publisher | |
Pages | 32 |
Release | 1965 |
Genre | Convergence |
ISBN |
Large Networks and Graph Limits
Title | Large Networks and Graph Limits PDF eBook |
Author | László Lovász |
Publisher | American Mathematical Soc. |
Pages | 495 |
Release | 2012 |
Genre | Mathematics |
ISBN | 0821890859 |
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
Topics in Discrete Mathematics
Title | Topics in Discrete Mathematics PDF eBook |
Author | Martin Klazar |
Publisher | Springer Science & Business Media |
Pages | 619 |
Release | 2007-05-28 |
Genre | Mathematics |
ISBN | 3540337008 |
This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.
Basic Applied Mathemetics for the Physical Sciences
Title | Basic Applied Mathemetics for the Physical Sciences PDF eBook |
Author | |
Publisher | Pearson Education India |
Pages | 484 |
Release | |
Genre | |
ISBN | 9788131706909 |
Random Graphs and Complex Networks
Title | Random Graphs and Complex Networks PDF eBook |
Author | Remco van der Hofstad |
Publisher | Cambridge University Press |
Pages | 341 |
Release | 2017 |
Genre | Computers |
ISBN | 110717287X |
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Random Graphs and Complex Networks: Volume 2
Title | Random Graphs and Complex Networks: Volume 2 PDF eBook |
Author | Remco van der Hofstad |
Publisher | Cambridge University Press |
Pages | 508 |
Release | 2024-02-08 |
Genre | Mathematics |
ISBN | 1316805581 |
Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.
Some Characterizations of a Simple Graph which is the Pointwise Limit of a Sequence of Continuous Simple Graphs
Title | Some Characterizations of a Simple Graph which is the Pointwise Limit of a Sequence of Continuous Simple Graphs PDF eBook |
Author | Wayne E. Schulz |
Publisher | |
Pages | 90 |
Release | 1970 |
Genre | Continuity |
ISBN |