| Description |
1 online resource (448 pages) |
| Series |
London Mathematical Society Lecture Note Series, 392 ; v. 392 |
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London Mathematical Society Lecture Note Series, 392
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| Contents |
Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Preface; Counting planar maps, coloured or uncoloured; 1 Introduction; 2 Definitions and notation; 2.1 Planar maps; 2.2 Power series; 2.3 The Potts model and the Tutte polynomial; 3 Uncoloured planar maps: the recursive approach; 3.1 A functional equation for planar maps; 3.2 More functional equations; Maps with prescribed face degrees; Eulerian maps with prescribed face degrees; Other families of maps; 3.3 Equations with one catalytic variable and algebraicity theorems; Algebraicity results |
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Where is the quadratic method?4 Uncoloured planar maps: bijections; 4.1 Two proofs from The Book?; Four-valent maps and blossoming trees; A more general construction; Quadrangulations and labelled trees; 4.2 More bijections; 5 Coloured planar maps: the recursive approach; 5.1 A functional equation for coloured planar maps; 5.2 More functional equations; 5.3 A linear case: bipolar orientations of maps; 5.4 A quasi-linear case: spanning trees; 5.5 When q is a Beraha number: Algebraicity; 5.6 The general case: differential equations; Comments; 6 Some bijections for coloured planar maps |
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6.1 Bipolar orientations of maps6.2 Spanning trees; 6.3 The Ising model (q = 2); 7 Final comments and questions; 7.1 Algebraicity; 7.2 Bijections; 7.3 Asymptotics of maps; Acknowledgements; References; A survey of PPAD-completeness for computing Nash equilibria; Acknowledgements; 1 Total Search Problems; 1.1 NP Total Search Problems; 1.2 Reducibility among total search problems; 1.3 PPAD, and some related concepts; 2 Sperner's lemma, and an associated computational problem; 3 Games and Nash Equilibria; 3.1 Some reductions among equilibrium problems; 3.2 The "in PPAD" result |
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3.3 The Algebraic Properties of Nash Equilibria4 Brouwer functions, and discrete Brouwer functions; 4.1 Discrete Brouwer functions; 5 From Discrete Brouwer functions to Games; 5.1 Graphical Games; 5.2 From graphical to normal-form games; 6 Easy and hard classes of games; 6.1 Hard equilibrium computation problems; 6.2 Polynomial-time equilibrium computation problems; 7 The Complexity of Path-following Algorithms; 8 From Games to Markets; References; Hypergraph Turán problems; Acknowledgements; 1 Introduction; 2 Basic arguments; 3 Hypergraph Lagrangians; 4 Link graphs and multigraphs |
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5 Stability6 Counting; 7 Flag algebras; 8 The remaining exact results; 9 Bounds for complete hypergraphs; 10 The infinitary perspective; 11 Algebraic methods; 12 Probabilistic methods; 13 Further topics; 13.1 Jumps; 13.2 Minimum degree problems; 13.3 Different host graphs; 13.4 Coloured Turán problems; 13.5 The speed of properties; 13.6 Local sparsity; 13.7 Counting subgraphs; 14 Summary of results; References; Some new results in extremal graph theory; Contents; 1 Introduction; 2 New results on classical extremal graph problems; 2.1 The extremal problems that are studied |
| Summary |
Survey articles based on the invited lectures given at the 23rd British Combinatorial Conference |
| Notes |
2.2 Erdos-Stone type problems |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Combinatorial analysis.
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Graph theory.
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MATHEMATICS -- Combinatorics.
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Combinatorial analysis
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Graph theory
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| ISBN |
9781139101196 |
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1139101196 |
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9781139099875 |
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1139099876 |
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9781139101851 |
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1139101854 |
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9781139004114 |
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1139004115 |
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