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E-grāmata: Topics in Algorithmic Graph Theory

Edited by (The Open University, Milton Keynes), Edited by (University of Haifa, Israel), Edited by (Purdue University, Indiana)
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Topics in Algorithmic Graph TheoryPalielināt
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Written by acknowledged international experts in the field, this book presents fifteen expository chapters in the rapidly expanding area of algorithmic graph theory. It serves graduate students and researchers in graph theory, combinatorics and computer science, as well as mathematicians and computer scientists in related fields.

Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.

Papildus informācija

This book presents fifteen carefully edited expository chapters in the rapidly expanding area of algorithmic graph theory.
Foreword xi
Martin Charles Golumbic
Preface xv
Preliminaries
1(334)
Lowell W. Beineke
Martin Charles Golumbic
Robin J. Wilson
1 Graph theory
1(7)
2 Connectivity
8(2)
3 Optimization problems on graphs
10(2)
4 Structured families of graphs
12(2)
5 Directed graphs
14(3)
1 Graph Algorithms
17(16)
Martin Charles Golumbic
1 Introduction
17(2)
2 Graph search algorithms
19(4)
3 Greedy graph colouring
23(1)
4 The structured graph approach
24(1)
5 Specialized classes of intersection graphs
25(8)
2 Graph Colouring Variations
33(19)
Alain Hertz
Bernard Ries
1 Introduction
33(1)
2 Selective graph colouring
34(4)
3 Online colouring
38(6)
4 Mixed graph colouring
44(8)
3 Total Colouring
52(16)
Celina M. H. De Figueiredo
1 Introduction
52(2)
2 Hilton's condition
54(1)
3 Cubic graphs
55(2)
4 Equitable total colourings
57(1)
5 Vertex-elimination orders
58(2)
6 Decomposition
60(2)
7 Complexity separation
62(2)
8 Concluding remarks and conjectures
64(4)
4 Testing Of Graph Properties
68(37)
Ilan Newman
1 Introduction
68(2)
2 The dense graph model
70(2)
3 Testing graph properties in the dense graph model
72(10)
4 Historical notes
82(4)
5 The incidence-list model
86(13)
6 Final comments
99(6)
5 Cliques, Colouring And Satisfiability: From Structure To Algorithms
105(25)
Vadim Lozin
1 Introduction
105(1)
2 Hereditary classes and graph problems
106(2)
3 From structure ...
108(9)
4 ... to algorithms
117(8)
5 Concluding remarks and open problems
125(5)
6 Chordal Graphs
130(22)
Martin Charles Golumbic
1 Introduction
130(2)
2 Minimal separators
132(1)
3 Perfect elimination
133(3)
4 Tree representations and clique-trees
136(1)
5 Superclasses of chordal graphs
137(5)
6 Subclasses of chordal graphs
142(3)
7 Applications of chordal graphs
145(2)
8 Concluding remarks
147(5)
7 Dually And Strongly Chordal Graphs
152(16)
Andreas Brandstadt
Martin Charles Golumbic
1 Introduction
152(1)
2 The hypergraph view of chordal graphs
153(3)
3 Dually chordal graphs
156(2)
4 Strongly chordal graphs
158(5)
5 Chordal bipartite graphs
163(5)
8 Leaf Powers
168(21)
Christian Rosenke
Van Bang Le
Andreas Brandstadt
1 Introduction
168(2)
2 Basic properties of leaf powers
170(3)
3 Recognition algorithms for leaf powers
173(5)
4 Classification and forbidden subgraphs
178(5)
5 Simplicial powers and phylogenetic powers
183(2)
6 Concluding remarks
185(4)
9 Split Graphs
189(18)
Karen L. Collins
Ann N. Trenk
1 Introduction
189(2)
2 Related classes of perfect graphs
191(2)
3 Degree sequence characterizations
193(1)
4 Ferrers diagrams and majorization
194(4)
5 Three-part partitions, NG-graphs and pseudo-split graphs
198(3)
6 Bijections, counting and the compilation theorem
201(2)
7 Tyshkevich decomposition
203(4)
10 Strong Cliques And Stable Sets
207(21)
Martin Milanic
1 Introduction
207(1)
2 Connections with perfect graphs
208(2)
3 CIS, general partition and localizable graphs
210(4)
4 Algorithmic and complexity issues
214(4)
5 Vertex-transitive graphs
218(2)
6 Related concepts and applications
220(4)
7 Open problems
224(4)
11 Restricted Matchings
228(18)
Maximilian Furst
Dieter Rautenbach
1 Introduction
228(1)
2 Basic results
229(2)
3 Equality of the matching numbers
231(4)
4 Hardness results
235(1)
5 Bounds
236(3)
6 Tractable cases
239(2)
7 Approximation algorithms
241(5)
12 Covering Geometric Domains
246(16)
Gila Morgenstern
1 Introduction
246(1)
2 Preliminaries
247(2)
3 The perfect graph approach
249(4)
4 Polygon covering problems
253(4)
5 Covering discrete sets
257(5)
13 Graph Homomorphisms
262(32)
Pavol Hell
Jaroslav Nesetril
1 Introduction
262(1)
2 Homomorphisms of graphs
263(1)
3 Homomorphisms of digraphs
264(2)
4 Injective and surjective homomorphisms
266(1)
5 Retracts and cores
267(2)
6 Median graphs and absolute retracts
269(2)
7 List homomorphisms
271(1)
8 Computational problems
271(4)
9 The basic homomorphism problem HOM(H)
275(2)
10 Duality
277(1)
11 Polymorphisms
278(4)
12 The list homomorphism problems LHOM(H)
282(2)
13 The retraction problems RET(H)
284(2)
14 The surjective versions SHOM(H), COMP(H)
286(1)
15 Conclusions and generalizations
287(7)
14 Sparsity And Model Theory
294(23)
Patrice Ossona De Mendez
1 Introduction
294(2)
2 There is depth in shallowness
296(5)
3 Orientation and decomposition
301(5)
4 Born to be wide
306(2)
5 Everything gets easier when you follow orders
308(2)
6 When dependence leads to stability
310(2)
7 Conclusion: can dense graphs be sparse?
312(5)
15 Extremal Vertex-Sets
317(18)
Serge Gaspers
1 Introduction
317(2)
2 Enumeration algorithms
319(4)
3 Lower bounds
323(3)
4 Measure & conquer
326(2)
5 Monotone local search
328(2)
6 Applications to exponential-time algorithms
330(2)
7 Conclusion
332(3)
Notes on contributors 335(5)
Index 340
Lowell W. Beineke is the Jack W. Schrey Professor Emeritus of Mathematics at Purdue University Fort Wayne. He has written over a hundred papers in graph theory and has served as Editor of The College Mathematics Journal. In addition to four previous volumes in this series, Robin Wilson and he have jointly edited five other books in the field. Recent honours include having an award of the College of Arts and Sciences at his university named after him, being entered into the Purdue University Book of Great Teachers, and receiving a Meritorious Service award from the Mathematical Association of America. He also received a Lifetime Service Award from Who's Who in America. Martin Charles Golumbic is an Emeritus Professor of Computer Science at the University of Haifa and founder of the Caesarea Edmond Benjamin de Rothschild Institute for Interdisciplinary Applications of Computer Science. He is the founding Editor-in-Chief of the journal Annals of Mathematics and Artificial Intelligence. The books he has written include Algorithmic Graph Theory and Perfect Graphs, Tolerance Graphs (with Ann Trenk), Fighting Terror Online: The Convergence of Security, Technology, and the Law and The Zeroth Book of Graph Theory: An Annotated Translation of Les Réseaux (ou Graphes) by André Sainte-Laguė. He is a Foundation Fellow of the Institute of Combinatorics and its Applications, a Fellow of the European Artificial Intelligence society EurAI, and a member of the Academia Europaea, honoris causa. Robin J. Wilson is an Emeritus Professor of Pure Mathematics at the Open University, UK, and of Geometry at Gresham College, London, and is a former Fellow of Keble College, Oxford. He has written and edited over forty books on graph theory, combinatorics and the history of mathematics, including Introduction to Graph Theory and Four Colours Suffice. A former President of the British Society for the History of Mathematics, he has won prizes from the Mathematical Association of America for his expository writing and was awarded the 2017 Stanton Medal of the Institute of Combinatorics and its Applications for his outreach activities in combinatorics.
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