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Extremal Graph Theory
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Book Synopsis Extremal Graph Theory by : Bela Bollobas
Download or read book Extremal Graph Theory written by Bela Bollobas and published by Courier Corporation. This book was released on 2013-07-02 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.
Book Synopsis Extremal Graph Theory with Emphasis on Probabilistic Methods by : Béla Bollobás
Download or read book Extremal Graph Theory with Emphasis on Probabilistic Methods written by Béla Bollobás and published by American Mathematical Soc.. This book was released on 1986 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. In this book, an update of his 1978 book Extremal Graph Theory, the author focuses on a trend towards probabilistic methods. He demonstrates both the direct use of probability theory and, more importantly, the fruitful adoption of a probabilistic frame of mind when tackling main line extremal problems. Essentially self-contained, the book doesnot merely catalog results, but rather includes considerable discussion on a few of the deeper results. The author addresses pure mathematicians, especially combinatorialists and graduate students taking graph theory, as well as theoretical computer scientists. He assumes a mature familiarity withcombinatorial methods and an acquaintance with basic graph theory. The book is based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984.
Book Synopsis Modern Graph Theory by : Bela Bollobas
Download or read book Modern Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising 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 flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs 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. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
Download or read book Graph Theory written by B. Bollobás and published by Elsevier. This book was released on 1982-01-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cambridge Graph Theory Conference, held at Trinity College from 11 to 13 March 1981, brought together top ranking workers from diverse areas of the subject. The papers presented were by invitation only. This volume contains most of the contniutions, suitably refereed and revised. For many years now, graph theory has been developing at a great pace and in many directions. In order to emphasize the variety of questions and to preserve the freshness of research, the theme of the meeting was not restricted. Consequently, the papers in this volume deal with many aspects of graph theory, including colouring, connectivity, cycles, Ramsey theory, random graphs, flows, simplicial decompositions and directed graphs. A number of other papers are concerned with related areas, including hypergraphs, designs, algorithms, games and social models. This wealth of topics should enhance the attractiveness of the volume.
Download or read book Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1
Book Synopsis Four Problems in Extremal Graph Theory by : Florian Pfender
Download or read book Four Problems in Extremal Graph Theory written by Florian Pfender and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extremal Graph Theory by : Béla Bollobás
Download or read book Extremal Graph Theory written by Béla Bollobás and published by Courier Corporation. This book was released on 2004-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ever-expanding field of extremal graph theory encompasses an array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume presents a concise yet comprehensive treatment, featuring complete proofs for almost all of its results and numerous exercises. 1978 edition.
Book Synopsis Topics in Extremal Graph Theory by : Brandon Cruz
Download or read book Topics in Extremal Graph Theory written by Brandon Cruz and published by . This book was released on 2009 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Problems in Extremal Graph Theory by : Kamil Popielarz
Download or read book Problems in Extremal Graph Theory written by Kamil Popielarz and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: .
Book Synopsis Pearls in Graph Theory by : Nora Hartsfield
Download or read book Pearls in Graph Theory written by Nora Hartsfield and published by Courier Corporation. This book was released on 2013-04-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
Download or read book Erdös on Graphs written by Fan Chung and published by CRC Press. This book was released on 2020-08-26 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Large Networks and Graph Limits by : László Lovász
Download or read book Large Networks and Graph Limits written by László Lovász and published by American Mathematical Soc.. This book was released on 2012 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Topics in Extremal Graph Theory by : Peter Keevash
Download or read book Topics in Extremal Graph Theory written by Peter Keevash and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extremal Graph Theory: Supersaturation and Enumeration by : Hong Liu
Download or read book Extremal Graph Theory: Supersaturation and Enumeration written by Hong Liu and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Extremal Graph Theory by : Myung Sook Chung
Download or read book Topics in Extremal Graph Theory written by Myung Sook Chung and published by . This book was released on 1993 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: New results are proved on several problems in extremal graph theory. Let $exsp*(D;H)$ denote the maximum number of edges in a connected graph with maximum degree D and no induced subgraph isomorphic to the graph H. It is shown that this is finite if and only if H is a disjoint union of paths. Several specific forbidden subgraphs H have been studied, and the following results have been proved: (1) $ exsp*(D;Psb4) = Dsp2$ for all D, uniquely achieved by $Ksb{D,D}.$ If, in addition, the maximum clique size is $omega$, then the number of edges is at most $Dsp2 - {D(omega-2)over 2}.$ (2) $exsp*(D;Psb5) = {2over 27}Dsp3 + O(Dsp2).$ (3) $exsp*(D;2Psb3) = {1over 8}Dsp4 +{1over 8}Dsp3 + O(Dsp2).$ (4) $exsp*(D;Psb3 + Psb2)
Book Synopsis Three Existence Problems in Extremal Graph Theory by : Paul S. Wenger
Download or read book Three Existence Problems in Extremal Graph Theory written by Paul S. Wenger and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Proving the existence or nonexistence of structures with specified properties is the impetus for many classical results in discrete mathematics. In this thesis we take this approach to three different structural questions rooted in extremal graph theory. When studying graph representations, we seek efficient ways to encode the structure of a graph. For example, an {it interval representation} of a graph $G$ is an assignment of intervals on the real line to the vertices of $G$ such that two vertices are adjacent if and only if their intervals intersect. We consider graphs that have {it bar $k$-visibility representations}, a generalization of both interval representations and another well-studied class of representations known as visibility representations. We obtain results on $mathcal{F}_k$, the family of graphs having bar $k$-visibility representations. We also study $bigcup_{k=0}^{infty} mathcal{F}_k$. In particular, we determine the largest complete graph having a bar $k$-visibility representation, and we show that there are graphs that do not have bar $k$-visibility representations for any $k$. Graphs arise naturally as models of networks, and there has been much study of the movement of information or resources in graphs. Lampert and Slater cite{LS} introduced {it acquisition} in weighted graphs, whereby weight moves around $G$ provided that each move transfers weight from a vertex to a heavier neighbor. Our goal in making acquisition moves is to consolidate all of the weight in $G$ on the minimum number of vertices; this minimum number is the {it acquisition number} of $G$. We study three variations of acquisition in graphs: when a move must transfer all the weight from a vertex to its neighbor, when each move transfers a single unit of weight, and when a move can transfer any positive amount of weight. We consider acquisition numbers in various families of graphs, including paths, cycles, trees, and graphs with diameter $2$. We also study, under the various acquisition models, those graphs in which all the weight can be moved to a single vertex. Restrictive local conditions often have far-reaching impacts on the global structure of mathematical objects. Some local conditions are so limiting that very few objects satisfy the requirements. For example, suppose that we seek a graph in which every two vertices have exactly one common neighbor. Such graphs are called {it friendship graphs}, and Wilf~cite{Wilf} proved that the only such graphs consist of edge-disjoint triangles sharing a common vertex. We study a related structural restriction where similar phenomena occur. For a fixed graph $H$, we consider those graphs that do not contain $H$ and such that the addition of any edge completes exactly one copy of $H$. Such a graph is called {it uniquely $H$-saturated}. We study the existence of uniquely $H$-saturated graphs when $H$ is a path or a cycle. In particular, we determine all of the uniquely $C_4$-saturated graphs; there are exactly ten. Interestingly, the uniquely $C_{5}$-saturated graphs are precisely the friendship graphs characterized by Wilf.
Book Synopsis Problems in Extremal Graph Theory by : André Kündgen
Download or read book Problems in Extremal Graph Theory written by André Kündgen and published by . This book was released on 1999 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
