Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
Download or read book Rainbow Connections of Graphs written by Xueliang Li and published by Springer Science & Business Media. This book was released on 2012-02-23 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject.
Download or read book Advanced Graph Theory and Combinatorics written by Michel Rigo and published by John Wiley & Sons. This book was released on 2016-11-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.
Download or read book Problems in Combinatorics and Graph Theory written by Ioan Tomescu and published by Wiley-Interscience. This book was released on 1985-04-30 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the most important combinatorial structures and techniques. This is a book of problems and solutions which range in difficulty and scope from the elementary/student-oriented to open questions at the research level. Each problem is accompanied by a complete and detailed solution together with appropriate references to the mathematical literature, helping the reader not only to learn but to apply the relevant discrete methods. The text is unique in its range and variety -- some problems include straightforward manipulations while others are more complicated and require insights and a solid foundation of combinatorics and/or graph theory. Includes a dictionary of terms that makes many of the challenging problems accessible to those whose mathematical education is limited to highschool algebra.
Download or read book COMBINATORICS AND GRAPH THEORY written by SARKAR and published by PHI Learning Pvt. Ltd.. This book was released on 2016-06-17 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and Graph Theory is designed as a textbook for undergraduate students of computer science and engineering and postgraduate students of computer applications. The book seeks to introduce students to the mathematical concepts needed to develop abstract thinking and problem solving—important prerequisites for the study of computer science. The book provides an exhaustive coverage of various concepts and remarkable introduction of several topics of combinatorics and graph theory. The book presents an informative exposure for beginners and acts as a reference for advanced students. It highlights comprehensive and rigorous views of combinatorics and graphs. The text shows simplicity and step-by-step concepts throughout and is profusely illustrated with diagrams. The real-world applications corresponding to the topics are appropriately highlighted. The chapters have also been interspersed throughout with numerous interesting and instructional notes. Written in a lucid style, the book helps students apply the mathematical tools to computer-related concepts and consists of around 600 worked-out examples which motivate students as a self-learning mode.KEY FEATURES Contains various exercises with their answers or hints. Lays emphasis on the applicability of mathematical structures to computer science. Includes competitive examinations’ questions asked in GATE, NET, SET, etc
Download or read book A First Course in Graph Theory and Combinatorics written by Sebastian M. Cioabă and published by Springer Nature. This book was released on 2022-07-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Download or read book Graph Theory Combinatorics Algorithms and Applications written by Y. Alavi and published by . This book was released on 1991 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Conference participants included research mathematicians and computer scientists from colleges, universities, and industry, representing various countries. China, which hosted the First International Conference in 1986, is particularly well-represented. The 58 contributions to this proceedings v
Download or read book Graph Theory Combinatorics and Algorithms written by Martin Charles Golumbic and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.
Download or read book Algorithmic Graph Theory written by Alan Gibbons and published by Cambridge University Press. This book was released on 1985-06-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to pure and applied graph theory with an emphasis on algorithms and their complexity.
Download or read book Combinatorial Enumeration of Groups Graphs and Chemical Compounds written by Georg Polya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1937 there appeared a paper that was to have a profound influence on the progress of combinatorial enumeration, both in its theoretical and applied aspects. Entitled Kombinatorische Anzahlbest immungen jUr Gruppen, Graphen und chemische Verbindungen, it was published in Acta Mathematica, Vol. 68, pp. 145 to 254. Its author, George Polya, was already a mathematician of considerable stature, well-known for outstanding work in many branches of mathematics, particularly analysis. The paper in Question was unusual in that it depended almost entirely on a single theorem -- the "Hauptsatz" of Section 4 -- a theorem which gave a method for solving a general type of enumera tion problem. On the face of it, this is not something that one would expect to run to over 100 pages. Yet the range of the applica tions of the theorem and of its ramifications was enormous, as Polya clearly showed. In the various sections of his paper he explored many applications to the enumeration of graphs, principally trees, and of chemical isomers, using his theorem to present a comprehen sive and unified treatment of problems which had previously been solved, if at all, only by ad hoc methods. In the final section he investigated the asymptotic properties of these enumerational results, bringing to bear his formidable insight as an analyst
Download or read book A Walk Through Combinatorics written by Mikl¢s B¢na and published by World Scientific. This book was released on 2006 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
Download or read book A Walk Through Combinatorics written by Miklós Bóna and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]. Sample Chapter(s) Chapter 1: Seven Is More Than Six. The Pigeon-Hole Principle (181 KB) Chapter 4: No Matter How You Slice It. The Binomial Theorem and Related Identities (228 KB) Chapter 15: Who Knows What It Looks Like,But It Exists. The Probabilistic Method (286 KB) Request Inspection Copy
Download or read book Matrices in Combinatorics and Graph Theory written by Bolian Liu and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.
Download or read book Geometric Graphs and Arrangements written by Stefan Felsner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Download or read book Applications of Combinatorics and Graph Theory to the Biological and Social Sciences written by Fred Roberts and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned.
Download or read book Computational Discrete Mathematics written by Sriram Pemmaraju and published by Cambridge University Press. This book was released on 2009-10-15 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.
Download or read book Thirty Essays on Geometric Graph Theory written by János Pach and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
