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Modern graph theory
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This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.Abstract:
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.read more
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Proceedings ArticleDOI
Graphs, matrix inequalities, and switching for the formation flying control of multiple spacecraft
Mehran Mesbahi,Fred Y. Hadaegh +1 more
TL;DR: In this article, the leader-following paradigm is used in the formation flying of multiple spacecraft in free space, using graph theory and linear matrix inequalities with logic-based switching.
Book ChapterDOI
Symmetries and the complexity of pure Nash equilibrium
TL;DR: It turns out that in all four classes of games Nash equilibria can be computed in TC0 when only a constant number of actions is available to each player, a problem that has been shown intractable for other succinct representations of multi-player games.
Journal ArticleDOI
Fidelity of the protein structure reconstruction from inter-residue proximity constraints.
TL;DR: This work shows that approximately 70% randomly selected constraints are sufficient for determining the fold of a domain (with an average root-mean-square deviation of
Journal ArticleDOI
Determinant identities for Laplace matrices
Elmar Teufl,Stephan Wagner +1 more
TL;DR: In this article, it was shown that every minor of an n × n Laplace matrix can be written in terms of those n 2 minors that are obtained by deleting two rows and corresponding columns.
Journal ArticleDOI
Linking the proteins--elucidation of proteome-scale networks using mass spectrometry.
Delphine Pflieger,Florence Gonnet,Sergio de la Fuente van Bentem,Heribert Hirt,Heribert Hirt,Alberto de la Fuente +5 more
TL;DR: The current state-of-the-art MS-based analytical pipelines for the purpose to characterize proteome-scale networks are reviewed.