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Author: Mark R. Budden
Publisher: Springer Nature
ISBN: 3031299817
Category : Mathematics
Languages : en
Pages : 102
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Book Description
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists. This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges. The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
Author: Mark R. Budden
Publisher: Springer Nature
ISBN: 3031299817
Category : Mathematics
Languages : en
Pages : 102
Get Book Here
Book Description
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists. This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges. The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
Author: Paul Erdős
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 528
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Book Description
Author: Frederick Hoffman
Publisher: Springer Nature
ISBN: 3031529693
Category :
Languages : en
Pages : 491
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Book Description
Author: Ding-Zhu Du
Publisher: Springer Nature
ISBN: 3030416720
Category : Computers
Languages : en
Pages : 298
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Book Description
This Festschrift is in honor of Ker-I Ko, Professor in the Stony Brook University, USA. Ker-I Ko was one of the founding fathers of computational complexity over real numbers and analysis. He and Harvey Friedman devised a theoretical model for real number computations by extending the computation of Turing machines. He contributed significantly to advancing the theory of structural complexity, especially on polynomial-time isomorphism, instance complexity, and relativization of polynomial-time hierarchy. Ker-I also made many contributions to approximation algorithm theory of combinatorial optimization problems. This volume contains 17 contributions in the area of complexity and approximation. Those articles are authored by researchers over the world, including North America, Europe and Asia. Most of them are co-authors, colleagues, friends, and students of Ker-I Ko.
Author: Zhao Zhang
Publisher: Springer Nature
ISBN: 3030576027
Category : Computers
Languages : en
Pages : 652
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Book Description
This volume constitutes the proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management, AAIM 2020, held in Jinhua, China in August 2020. The 39 full papers and 17 short papers presented were carefully reviewed and selected from 76 submissions. The papers deal with emerging important algorithmic problems with a focus on the fundamental background, theoretical technology development, and real-world applications associated with information and management analysis, modeling and data mining. Special considerations are given to algorithmic research that was motivated by real-world applications.
Author: John Harris
Publisher: Springer Science & Business Media
ISBN: 0387797114
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Manoj Changat
Publisher: Springer Nature
ISBN: 3030392198
Category : Mathematics
Languages : en
Pages : 497
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Book Description
This book constitutes the proceedings of the 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020, held in Hyderabad, India, in February 2020. The 38 papers presented together with 2 invited talks in this volume were carefully reviewed and selected from 102 submissions. The papers are organized in topical sections on graph algorithms, graph theory, combinatorial optimization, distributed algorithms, combinatorial algorithms, and computational complexity.
Author: Ronald L. Graham
Publisher: John Wiley & Sons
ISBN: 9780471500469
Category : Mathematics
Languages : en
Pages : 230
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Book Description
Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theorywill find this illuminating..." --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah's proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey's fundamental paper from 1930 andErdos' and Szekeres' article from 1935, while placingthe various theorems in the context of T. S. Motzkin'sthought on the subject of "Complete Disorder isImpossible." Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outside applications, RamseyTheory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulousscales * Extentions and implications of van der Waerden's Theorem,the Hales-Jewett Theorem, Roth's Theorem, Rado'sTheorem, Szemeredi's Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems andequations * Special cases and broader interdisciplinary applications ofRamsey Theory principles An invaluable reference for professional mathematicians workingin discrete mathematics, combinatorics, and algorithms, RamseyTheory, Second Edition is the definitive work on thesubject.
Author: Jaroslav Nešetřil
Publisher: Springer Nature
ISBN: 3030838234
Category : Mathematics
Languages : en
Pages : 875
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Book Description
This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.
Author: Remco van der Hofstad
Publisher: Cambridge University Press
ISBN: 110717287X
Category : Computers
Languages : en
Pages : 341
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Book Description
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
