Algorithmic Graph Theory and Perfect Graphs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algorithmic Graph Theory and Perfect Graphs write by Martin Charles Golumbic. This book was released on 2014-05-10. Algorithmic Graph Theory and Perfect Graphs available in PDF, EPUB and Kindle. Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.
Submodular Functions and Electrical Networks
Submodular Functions and Electrical Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Submodular Functions and Electrical Networks write by H. Narayanan. This book was released on 1997-05. Submodular Functions and Electrical Networks available in PDF, EPUB and Kindle. There is a strong case for electrical network topologists and submodular function theorists being aware of each other's fields. Presenting a topological approach to electrical network theory, this book demonstrates the strong links that exist between submodular functions and electrical networks. The book contains: . a detailed discussion of graphs, matroids, vector spaces and the algebra of generalized minors, relevant to network analysis (particularly to the construction of efficient circuit simulators) . a detailed discussion of submodular function theory in its own right; topics covered include, various operations, dualization, convolution and Dilworth truncation as well as the related notions of prinicpal partition and principal lattice of partitions. In order to make the book useful to a wide audience, the material on electrical networks and that on submodular functions is presented independently of each other. The hybrid rank problem, the bridge between (topological) electrical network theory and submodular functions, is covered in the final chapter. The emphasis in the book is on low complexity algorithms, particularly based on bipartite graphs. The book is intended for self-study and is recommended to designers of VLSI algorithms. More than 300 problems, almost all of them with solutions, are included at the end of each chapter.
Threshold Graphs and Related Topics
Threshold Graphs and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Threshold Graphs and Related Topics write by N.V.R. Mahadev. This book was released on 1995-09-13. Threshold Graphs and Related Topics available in PDF, EPUB and Kindle. Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field.
Recent Results in the Theory of Graph Spectra
Recent Results in the Theory of Graph Spectra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Results in the Theory of Graph Spectra write by D.M. Cvetkovic. This book was released on 1988-01-01. Recent Results in the Theory of Graph Spectra available in PDF, EPUB and Kindle. The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2.Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.
Submodular Functions and Optimization
Submodular Functions and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Submodular Functions and Optimization write by Satoru Fujishige. This book was released on 2005-07-26. Submodular Functions and Optimization available in PDF, EPUB and Kindle. It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. - Self-contained exposition of the theory of submodular functions - Selected up-to-date materials substantial to future developments - Polyhedral description of Discrete Convex Analysis - Full description of submodular function minimization algorithms - Effective insertion of figures - Useful in applied mathematics, operations research, computer science, and economics
