Random Graphs '83

Random Graphs '83
Author: A. Rucinski
Publisher: Elsevier
Total Pages: 375
Release: 2011-10-10
Genre: Mathematics
ISBN: 0080872298

The range of random graph topics covered in this volume includes structure, colouring, algorithms, mappings, trees, network flows, and percolation. The papers also illustrate the application of probability methods to Ramsey's problems, the application of graph theory methods to probability, and relations between games on graphs and random graphs.

Introduction to Random Graphs

Introduction to Random Graphs
Author: Alan Frieze
Publisher: Cambridge University Press
Total Pages: 483
Release: 2016
Genre: Mathematics
ISBN: 1107118506

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Random Graphs

Random Graphs
Author: Svante Janson
Publisher: John Wiley & Sons
Total Pages: 350
Release: 2011-09-30
Genre: Mathematics
ISBN: 1118030966

A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references

Random Graphs

Random Graphs
Author: V. F. Kolchin
Publisher: Cambridge University Press
Total Pages: 266
Release: 1999
Genre: Mathematics
ISBN: 0521440815

Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.

Random Graphs

Random Graphs
Author: Béla Bollobás
Publisher: Cambridge University Press
Total Pages: 520
Release: 2001-08-30
Genre: Mathematics
ISBN: 9780521797221

This is a revised and updated version of the classic first edition.

Random Graph Dynamics

Random Graph Dynamics
Author: Rick Durrett
Publisher: Cambridge University Press
Total Pages: 203
Release: 2010-05-31
Genre: Mathematics
ISBN: 1139460889

The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Random Graphs and Networks: A First Course

Random Graphs and Networks: A First Course
Author: Alan Frieze
Publisher: Cambridge University Press
Total Pages: 234
Release: 2023-03-09
Genre: Mathematics
ISBN: 1009260316

Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.

Random Graphs and Complex Networks

Random Graphs and Complex Networks
Author: Remco van der Hofstad
Publisher: Cambridge University Press
Total 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.

Erdös Centennial

Erdös Centennial
Author: László Lovász
Publisher: Springer Science & Business Media
Total Pages: 714
Release: 2014-01-24
Genre: Mathematics
ISBN: 3642392865

Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.

Erdös on Graphs

Erdös on Graphs
Author: Fan Chung
Publisher: CRC Press
Total Pages: 248
Release: 2020-08-26
Genre: Mathematics
ISBN: 1000151816

This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines the legacy of open problems he left to the world after his death in 1996.