Author: TeresaW. Haynes Publisher: Routledge ISBN: 1351454641 Category : Mathematics Languages : en Pages : 519
Book Description
""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.
Author: Michael A. Henning Publisher: Springer Science & Business Media ISBN: 1461465257 Category : Mathematics Languages : en Pages : 184
Book Description
Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is an excellent resource for students interested in beginning their research in this field. Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems.
Author: Ding-Zhu Du Publisher: Springer Science & Business Media ISBN: 1461452422 Category : Business & Economics Languages : en Pages : 206
Book Description
The connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, especially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. In this book, we are going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets. The book consists of 16 chapters. Except the 1st one, each chapter is devoted to one problem, and consists of three parts, motivation and overview, problem complexity analysis, and approximation algorithm designs, which will lead the reader to see clearly about the background, formulation, existing important research results, and open problems. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics.
Author: Teresa W. Haynes Publisher: CRC Press ISBN: 1482246589 Category : Mathematics Languages : en Pages : 465
Book Description
"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."
Author: Gary Chartrand Publisher: Chapman and Hall/CRC ISBN: 9780412987212 Category : Mathematics Languages : en Pages : 432
Book Description
This is the third edition of the popular text on graph theory. As in previous editions, the text presents graph theory as a mathematical discipline and emphasizes clear exposition and well-written proofs. New in this edition are expanded treatments of graph decomposition and external graph theory, a study of graph vulnerability and domination, and introductions to voltage graphs, graph labelings, and the probabilistic method in graph theory.
Author: Fedor V. Fomin Publisher: Cambridge University Press ISBN: 1107057760 Category : Computers Languages : en Pages : 531
Book Description
A complete introduction to recent advances in preprocessing analysis, or kernelization, with extensive examples using a single data set.
Author: Marek Cygan Publisher: Springer ISBN: 3319212753 Category : Computers Languages : en Pages : 618
Book Description
This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
Author: Jaroslav Nešetřil Publisher: Springer Science & Business Media ISBN: 3642278752 Category : Mathematics Languages : en Pages : 472
Book Description
This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.
Author: Kenneth I. Appel Publisher: American Mathematical Soc. ISBN: 0821851039 Category : Mathematics Languages : en Pages : 760
Book Description
In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Author: TeresaW. Haynes
Author: Michael A. Henning
Author: Fedor V. Fomin
Author: Ding-Zhu Du
Author: Teresa W. Haynes
Author: Gary Chartrand
Author: Fedor V. Fomin
Author: Marek Cygan
Author: Jaroslav Nešetřil
Author: Kenneth I. Appel